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Atoms are the basis of existence. has been suggested from the time of early Indian or Greek Philosophers (400 B.C.)¬†who believed that atoms were the basic components of matter.¬†In their view, continual subdivision of matter would eventually result in atoms that could not further be divisible.¬†The term ‘atom’ originates in the Greek word ‘atomio’ that refers to ‘uncutable’ or ‘non-divisible’.¬†These ideas at the time were only ideas that were not supported by any method of testing them.¬†These theories remained untested for a long time , and were revived by scientists in the late nineteenth century.¬†The theory of the atomic structure of matter was first put forward on a solid base of science by John Dalton, a British teacher at a school in 1808.¬†Dalton’s theory, also known as Dalton’s atomic theories, believed in the atom as being the most fundamental quantum particle in matter (Unit 1).Best JEE Coaching in Aizwal. Dalton’s theory of the atom was able explain the laws on conversation of the mass, the mas of constant composition and law of multiple effectively.

However, it was unable to explain the results of numerous tests, for instance, it was discovered that certain substances like ebonite and glass touched with fur or silk are charged electrically.¬†This unit begins with the observations made by scientists at the end of the nineteenth century and the beginning of the 20th century.¬†They proved the fact that atoms are composed of sub-atomic particles i.e. neutrons, protons, and electrons — a notion that is quite different from the one of Dalton.¬†The discovery of sub-atomic PARTICLES An understanding of the structure of an atom was discovered through studies on the electrical discharge of gasses.¬†Before discussing these results, it is important to remember a basic rule of behavior for charged particles “Like charges repel one another and opposite charges draw one another”.¬†Discovery of Electron In 1830, Michael Faraday showed that when electricity is transferred through an electrolyte’s solution chemical reaction takes place on the electrodes that led to the release and deposition on the electrodes.¬†

He proposed a few laws, which you’ll learn in class XII.¬†These findings suggested the fragmented electrical nature.¬†By the mid-1850s, many scientists, primarily Faraday began to research discharges of electricity within partially evacuated tube called cathode ray discharge tubes.¬†It is shown in Fig.¬†2.1.¬†A cathode ray tube comprised of glass with two small pieces of metal, referred to as electrodes, that are sealed inside.¬†The electric discharge from the gasses could be seen only at extremely low pressures, and at extremely high voltages.¬†The gas’s pressure could be adjusted through the removal of the glass tube.¬†If a sufficiently high voltage is applied to the electrodes, the current starts moving through a flow of particles that move through the tubes, from the electrode that is negative (cathode) and on to the positively charged electrode (anode).¬†They were known as cathode radiation or cathode particle¬†rays.¬†Best JEE Coaching in Aizwal.

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The circulation of the current from cathode to the anode was then examined by drilling holes in the anode, and then covering the tube behind the anode with phosphorescent material , zinc sulfur.¬†If these rays, upon passing through the anode, hit the zinc sulphide layer, the coating forms a bright spot upon the coated surface. [Fig.¬†2.1(b)].¬†Fig.¬†2.1(a) A cathode ray discharge tube Fig.¬†2.1(b) An cathode discharge tube having a perforated anode. The results of these experiments are summarized below.¬†(i) Cathode’s rays originate from the cathode, and then move to anode.¬†(ii) The rays themselves aren’t visible, however their behavior can be observed through the use of certain kinds material (fluorescent or phosphorescent) which emit light when struck by their rays.¬†TV picture tubes can be described as cathode-ray tubes. Television pictures are because of fluorescence on the screen of the TV that is covered with specific materials that are fluorescent or phosphorescent.¬†Best JEE Coaching in Aizwal.

(iii) Without an any electrical and magnetic fields, the light rays are unidirectional lines (Fig.¬†2.2).¬†(iv) When there’s an an electrical magnetic or electrical field, the behavior of cathode-rays is like that of positively charged particles, indicating that the cathode’s rays consist of positively charged particles known as electrons.¬†(v) The properties of cathode radiations (electrons) are not dependent on the electrode’s material as well as the nature of the gas in the cathode tube for rays.¬†We can therefore be sure that electrons form the the primary component of all molecules.¬†2.1.2 Rate of Charge to Mass of the Electron in 1897 British physical scientist J.J. Thomson determined the ratio between electric charged (e) and the electron’s mass (me ) by employing a cathode ray tubes using an electrical and magnetic fields perpendicular to each other, as well as to electrons’ paths (Fig.¬†2.2).¬†If only an electric field applied electrons diverge from their path and strike the cathode tube at the point A (Fig.¬†2.2).¬†

In the same way, with magnetic field only used, electron is struck by the cathode-ray tube at the point C. By carefully balancing magnetic and electric field strengths you can return the electron on the path that it follows in the absence of an electric or magnetic field. Then they strike the screen at location B. Thomson argued that the amount of deviation of particles from their paths when they encounter an electrical or magnetic field is dependent on: (i) the magnitude of the negative charge that is imposed on the particle. The higher the force of charged particle the greater will be the interactions with magnetic or electric field, which in turn increases the deflection.¬†(ii) the mass of the particleheavier particles, more deflection.¬†(iii) intensity of magnetic or electric field -the electrons’ deflection from their original direction increases with the increase of the voltage that is applied to electrodes or the force of magnetic fields.¬†Best JEE Coaching in Aizwal.

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¬†Through precise analysis of the magnitude of deflections that are observed by electrons in the strength of the electric field (or magnetic field strength) Thomson was able to calculate that e/me’s value the following: e e.m = 1.758820 1011 C kg-1 (2.1) where me is the electron’s mass in kilograms, and e represents the size of the charge that the electron has on it in the form of coulomb (C).¬†As electrons carry negative charges the charge of electron is -e.¬†2.1.3 Charge of the Electron R.A. Millikan (1868-1953) invented a method, known as the oil drop experiments (1906-14) to measure the electron’s charge.¬†Millikan discovered that the charge of electrons to be 1.6 10- 19 C.¬†Best JEE Coaching in Aizwal.The current accepted electrical charge is 1.602176 10-19 C. The mass of the electron (me ) was calculated by combining these findings with Thomson’s the e/me ratio.2.1.4 The discovery of Protons and Neutrons Electrical discharges that were carried out inside the modified cathode-ray tube led to the discovery of rays from canals that carried positive charged particles.¬†The properties that these particles have are described below.

 (i) Contrary to cathode radiations the mass of particles that are positively charged varies on the gas inside the cathode ray tube. They are simply positively charged gaseous particles. (ii) The mass-to-charge ratio of particles is dependent upon the source of gas where they come from. (iii) Certain positively charged particles have one more than the basic electrical charge. (iv) The behavior of these particles when they are in the electric or magnetic field is different from that observed in cathode or electron radiations. The tiniest and lightest positive ion was made from hydrogen, and was dubbed proton. The positive charged particle was discovered in 1919. Then, a demand was recognized for the existence of a neutral electrical charge as one of the elements of an atom. The particles were identified through Chadwick (1932) after bombarding a thin piece of beryllium with particles called a-particles. Electronally neutral particles with an average mass of the protons were released, they were.

¬†They were referred to as neutrons.¬†The main properties of the fundamental particles are described in Table 2.1.¬†2.2 ATOMIC MODELS Observations obtained from the research described in the preceding sections suggest Dalton’s indivisible Atom is comprised of sub-atomic particles that carry negative and positive charges.¬†The most significant issues for researchers after the discovery of subatomic particles was to: * determine the stability of the atoms, * to study the properties of elements with respect to the chemical and physical properties Millikan’s Oil Drop Method. In this method drops of oil as mist created by the atomiser were allowed to flow through a tiny gap in the upper plate of an electrical condenser.¬†Best JEE Coaching in Aizwal.The downward movement of these droplets was seen by a telescope equipped with a micrometer-sized eyepiece.¬†Through measuring the speed of droplets falling, Millikan was able to determine the weight of droplets of oil.¬†The air in is ionized using X-rays to pass through it.¬†

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The charge that was generated by the droplets of oil was accumulated through collisions with gaseous ions.¬†The drop of charged droplets may be delayed, accelerated, or even stopped depending on the charge that the droplets carry as well as the strength and polarity of the voltage that is applied to the plates.¬†Through careful examination of the effects of the electrical force on movement of oil droplets Millikan found that the amount of the electrical charge, q on the droplets remains an integral number of electric charge the e, which means that Q = n e where the n is 1,2 3… .¬†Fig.¬†2.3 Figure 2.3. Millikan oil drop device to measure charge “e”.¬†In the chamber the forces acting on the oil drop are electrostatic, gravitational, due to an the electrical field, and an acoustic drag force as the drop moves.¬†* to explain the creation of various types of molecules through the combination of different atoms. to better understand the cause and the nature of electromagnetic radiation absorbed by or emitting by atoms.¬†Best JEE Coaching in Aizwal.

Different models of atomic structure were developed to explain the patterns of charged particles within an atom. While certain models failed to describe the stability and stability of an atom two of them that were that was proposed in 1898 by J.J. Thomson and the one suggested in the work of Ernest Rutherford are discussed below. 2.2.1 Thomson Model of Atom J. J. Thomson in 1898, suggested that atoms have an spherical form (radius around 10-10m) where charges are evenly dispersed. The electrons are incorporated into the atom in such a way that it provides the most secure electrical arrangement (Fig. 2.4). There are many different names given for this type of model. such as for instance, plum pudding watermelon, or raisin pudding. The model could be described as the second part of the nineteenth century, various types of rays were identified, apart from those mentioned earlier.Wilhalm Roentgen (1845-1923) in 1895 proved that electrons striking an element in cathode tubes, they create the rays that create fluorescence in material that is placed outside of the cathode tubes. 

Because Roentgen was unaware of what the source of radiation was, he called them X-rays . The name remains in use. It was observed that X-rays are generated by electrons striking the metal anode. They are also known as targets. They are not affected by magnetic or electric fields, and possess a powerful penetrating force through material, which is why they are utilized to investigate the inside of objects. They are extremely small durations (~0.1 millimeters) and have an electro-magnetic nature (Section 2.3.1). Best JEE Coaching in Aizwal. Henri Becqueral (1852-1908) observed that certain elements that emit radiation by themselves and referred to this phenomenon as radioactivity. These elements are also known by their radioactive properties. This field was invented in the late 1800s by Marie Curie, Piere Curie, Rutherford and Fredrick Soddy. It was found that three types of radiations i.e. A as well as b- and g-rays emit. Rutherford discovered that a-rays are composed of high-energy particles that carry two positive charge units and four units of mass. He concluded that the aparticle is helium. 

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Thomson model of atom depicted as a pudding or watermelon that has positive charge that has seeds or plums (electrons) in it.¬†A key feature to this type of model is that its mass thought to be evenly distributed across the entire atom.¬†While this model did explain the neutrons of the atom but it did not match the findings of subsequent studies.¬†Thomson was awarded the Nobel Prize for physics in 1906, in recognition of his research and theories regarding the transmission of electricity through gases.nuclei can be described as the result of A- particles teamed up with two electrons produced Helium gas.¬†B-rays are negatively charged particles that are similar to electrons.¬†G-rays are extremely powerful radiations such as X-rays. They’re neutral and do not comprise particles.¬†In terms of penetrating power, particles are the least powerful and are followed by B-rays (100 times the power of particles of the type a) and G-rays (1000 times that of particles).¬†Rutherford’s Nuclear Model of Atom Rutherford and his students (Hans Geiger and Ernest Marsden) bombarded very thin gold foils with A-particles.Best JEE Coaching Centre in Aizwal.¬†

Rutherford’s famous experiment with a-particle scattering can be seen in Fig.¬†2.5.¬†A stream of high-energy particles from a source of radioactivity was directed towards a thin foil (thickness of 100 nm) that was made from gold.¬†The gold foil thin contained a circular, Zs sulphide-fluorescent screen that was surrounded by it.¬†When a particle struck upon the screening, small flash of light appeared at that moment.¬†The results of the scattering experiment were rather surprising.¬†Based on the Thomson model of the atom the weight of each gold atom that is in the foil must be distributed evenly across the entire atom. particles with enough energy to move directly through a homogenous pattern of mass.¬†It was expected that particle would change direction and alter direction only by small angles when they passed over the metal.¬†It was found that: (i) majority of the particles went through the foil unaffected.¬†(ii) A small portion of the particles was affected by small angles.¬†(iii) A small number of particles (~1 per the 20,000) bounced back which is, they were deflected by almost 180deg .¬†

Based on the findings, Rutherford drew the following conclusions about the structure of the Atoms: (i) Most of the atom’s space is empty because the majority of the a-particles travelled through the foil unimpeded.¬†(ii) A small number of positively charged a-particles were redirected.¬†The reason for the deflection could be due to a huge repulsive force indicating it is not the case that positive charges of the atom isn’t dispersed throughout the atom like Thomson believed.¬†The positive charge must concentrate in a tiny volume that repels and deflected positively charged particles.¬†(iii) Calculations made by Rutherford revealed that the area occupied by the nucleus is tiny in comparison to the overall size of an atom.¬†The radius of an Atom is around 10-10m in comparison to the radius of the nucleus, which is about 10-15 meters. It is possible to appreciate the differences in size by understanding that if a cricket ball is a nucleus the radius of the nucleus would be around 5 kilometers.¬†Based on these observations and conclusions Rutherford suggested the nuclear model of the atom.¬†Best JEE Coaching Centre in Aizwal.¬†

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Based on the model (i) Positive charge, and the bulk of the mass in the atom was concentrated in an tiny areas.¬†This small part that made up the nucleus of the atom referred to as the nucleus according to Rutherford.¬†(ii) Nucleus enclosed by electrons which move through the nucleus at rapid speed, in circular pathways called orbits.¬†Therefore, Rutherford’s concept of an atom is similar to that of the solar system where the nucleus performs the role of the sun and the electrons play the role play the role of planets that rotate.¬†(iii) Electrons as well as the nucleus are bonded with electrostatic attraction forces.¬†2.2.3 Nuclear Numbers and Mass Numeric The existence of positive charge in the nucleus can be explained by the protons that reside in the nucleus.¬†In the past the charge of proton is the same however it is opposite to the charge of an electron.¬†The number of proton present in the nucleus is equivalent to the atomic number (Z ).¬†Best JEE Coaching Centre in Aizwal.¬†

 In this case it is said that the amount of protons within the hydrogen nucleus is one while in the sodium atom, it is 11. Therefore, their number in the atomic nucleus is 1 and 11, respectively. To ensure electro-neutrality in the electrical field, the number electrons inside an atom will be the same as that of the protons (atomic number Z ). In this case, the number of electrons within hydrogen atoms and sodium atoms are 11 and 1 respectively. The number of atoms (Z) = the number of protons present in the nucleus of the atom the number of electrons that make up the nuetral atom (2.3) In contrast, the positive charge in the nucleus is caused by protons, it is the mass of the nucleus is caused by neutrons and protons. The neutrons and protons that are present in the nucleus, are collectively referred to as nucleons. The amount of nucleons can be described as the mass numbers (A) for the entire atom. 

Mass number (A) is the sum of the number of proton (Z) + the number of neutrons (n) (2.4) 2.2.4 Isobars and Isotopes of an atom may be represented using the symbol for elements (X) with superscript on the left right side of the symbol as an atomic mass (A) as well as an underscript (Z) to the right hand side to represent the Atomic number (i.e. the atomic number is A Z). Isobars are those atoms having the identical mass numbers but with a different atomic numbers, for instance 6 14C or 7 14N. However those atoms having the same number of atoms, but with different mass number are called isotopes. In the sense of (according the equation 2.4) It is clear that the difference between isotopes can be attributed to the existence of a various numbers of neutrons within the nucleus. In the case of hydrogen atoms, 99.985% of hydrogen atoms have only one proton. Best JEE Coaching Centre in Aizwal. The isotope that is protium is known as (1 1H). 

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The remainder of the percent of hydrogen atoms contains two additional isotopes. The one with one neutron and one proton is known as the deuterium ( 1 2 D 0.015 percent) while the second isotope that contains 2 neutrons and 1 proton is known as tritium (1 3 T ). This isotope can be found in small amounts on earth. Other examples of common isotopes include carbon atoms that contain 7, and 8 neutrons, in addition to six protons ( 6 12 6 13 6 6 14 C, C, C ) and chlorine atoms that contain 19 and 20 neutrons in addition to seventeen protons ( 1735 1737 Cl ). The last thing to be noted about isotopes is that the chemical properties of atoms are influenced by the amount of electrons. Best JEE Coaching Centre in Aizwal. These are determined by the amount of protons found in the nucleus. The quantity of neutrons that are present within the nucleus have little impact upon the chemical characteristics of the element. So, all isotopes of an element exhibit the same chemical behavior.

2.2.5 Drawbacks of the Rutherford Model As you’ve read in the previous paragraphs, Rutherford nuclear model of an atom is similar to the solar system on a smaller scale where the nucleus plays the role of the Classical mechanics can be described as a theoretic science that is based on Newton’s motion laws.¬†It outlines the rules of motion for macroscopic objects.¬†The massive sun and electrons, which are similar to smaller planets.¬†If classical mechanicsapplies on the solar system it proves that the planets have precise circular orbits about the sun.¬†The gravitational force that exists between the planets is represented by the formula G. 1 2 2 1 2 2 m m rwhere m1 and M2 are the mass and it is the distance of distance between the masses while G represents the gravity constant.¬†The theory also allows for calculation of precisely the orbits of planets and they are in line with observations made by scientists.¬†The closeness to the solar model and the the nuclear models suggests that the electrons will travel around the nucleus on precise orbits.

Additionally, there is there is a coulomb force (kq1q2/r2 in which q1 and 2 are the charges and the distance r is the between the charges, as well as k being the constant of proportionality) between the electron and nucleus is mathematically comparable with the force of gravitation.¬†But, when a body is in orbit, it experiences acceleration even when it’s moving at a constant speed in its orbit because of the changing direction.¬†Therefore, any electron that is part of the model that describes the planet’s orbits is in acceleration.¬†Based on the theory of electromagnetics developed by Maxwell charged particles that are accelerate should produce electromagnetic energy (This phenomenon is not the case for planets because they do not have charges).¬†Thus, an electron within an orbit emits radiation. The energy carried by radiation is derived from electronic motion.¬†Thus, the orbit will shrink over time.Best JEE Coaching Centre in Aizwal.¬†

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¬†Calculations indicate that it should be just 10-8 seconds to enter the nucleus.¬†However, this isn’t the case.¬†So the Rutherford model does not describe the stable nature of an atom.¬†If the motion of electrons is explained on the basis of the classical electromagnetic theory and mechanics You might ask because the movement of electrons’ orbit is causing the instability of the atom it is not logical to treat electrons as being stationary within the nucleus.¬†If electrons were stationary and electrostatic attraction was present between the nucleus’s dense structure and electrons would pull the electrons towards the nucleus, forming an atomic miniature of Thomson’s model of the atom.¬†A major drawback to this Rutherford theory is the fact that it does not provide any information about the distribution of electrons within the nucleus, or the energy levels associated with these electrons.¬†2.3 Developments leading to the BOHR’S MODEL of ATOM The past, the results gathered from studies of the interactions between radiations and matter have revealed a wealth of information about how atoms are structured as well as molecules.¬†

Neils Bohr utilised these results to enhance the model suggested by Rutherford.¬†Best JEE Coaching Centre in Aizwal.¬†Two key developments played a crucial part in the development of Bohr’s model for the atom.¬†These included: (i) Dual character of electromagnetic radiation, which implies that the radiation has particles and wave similar characteristics as well as (ii) experimental results concerning the atomic spectra.¬†We will first talk the dual character of the electromagnetic radiation.¬†The experimental results related to the atomic spectra will be reviewed in section 2.4.¬†2.3.1 The nature of waves in Electromagnetic Radiation During the late nineteenth century, scientists were studying the radiation absorption and emission from objects that were heated.¬†They were referred to as thermal radiations.¬†They wanted to know the cause of how the radiation is produced.¬†It’s now a known reality that the thermal radiations are made up of electromagnetic waves with various frequency or wavelengths.¬†

It is based upon various modern theories that were undiscovered in the late nineteenth century.¬†The first active investigation into thermal radiation laws was conducted in the 1850’s , and the idea of electromagnetic waves as well as the emission of electromagnetic waves caused by charged particles that accelerate was first developed in the 1800’s, by James Clerk Maxwell, which was later confirmed by experiments in the 1880’s by Heinrich Hertz.¬†In this article, we will discover some basic facts about electromagnetic radiations.¬†James Maxwell (1870) was the first to offer an extensive explanation of the interaction between charged bodies as well as the behavior of magnetic and electrical fields at the macroscopic level.¬†Maxwell suggested that when an the electrically charged particle is moving through accelaration, oscillating magnetic and electrical fields are created and transferred.¬†The fields are then sent out in the form of electromagnetic waves, also known as electromagnetic radiation.¬†Top JEE Coaching Centre in Aizwal.¬†

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Light is the type of radiation which has been observed since earlier times, and speculation on its nature goes back to the time of ancient civilizations.¬†In earlier times (Newton) lights were thought to be composed from particle (corpuscules).¬†It was not until the 19th century that the light’s nature as a wave was recognized.¬†Maxwell was also the first to discover that light waves have a connection with oscillating electrical and magnetic nature. Although the electromagnetic wave is extremely complex it is worth examining just a few basic properties.¬†Top JEE Coaching Centre in Aizwal.¬†(i) The magnetic and electric fields that oscillate generated by charged particles oscillating are perpendicular to one another and are both in the same direction as the the propagation of the wave.¬†An illustration of the electromagnetic wave can be seen in Figure.¬†2.6.¬†(ii) In contrast to the sound waves that are produced in water electromagnetic waves don’t require a medium to move and are able to travel through vacuum.¬†(iii) There is widely accepted that there exist numerous kinds of electromagnetic radiation that differ in the wavelength (or frequency).¬†

This is known as the electromagnetic spectrum (Fig.¬†2.7).¬†Different spectrum regions are identified with different names.¬†Examples include radio frequency region of 10 Hz, utilized for broadcasting; microwave area that is around 1010 Hz, which is that is used for radar; infrared area that is around 1013 Hz, utilized for heating; ultraviolet region around 1016Hz , a component of the sun’s radiation.¬†The portion that is around 1015 Hz is typically referred to as visible light.¬†This is the only portion that our eyes detect (or be able to detect).¬†Special instruments are needed to detect invisible radiation.¬†Fig.¬†2.7 (a) the spectrum of electromagnetic radiation.¬†(b) Spectrum visible.¬†The visible region comprises only an insignificant portion of the total spectrum.¬†(iv) Different types and types of measurements are employed to describe electromagnetic radiation.¬†The electromagnetic radiations are characterized by their properties, specifically the frequency (n ) and the wavelength (l).¬†Its SI measurement used to measure the frequency (n) is called hertz (Hz, 1) following Heinrich Hertz.¬†

It’s defined as the amount of waves passing through at a specific point within a second.¬†The units of measurement for wavelength must be in the form of length. You are aware, the SI length units are meters (m).¬†Because electromagnetic radiation is composed of various kinds of waves with shorter wavelengths which is why smaller units are employed.¬†Fig.2.7 illustrates different kinds of electromagnetic radiations, which differ from each other in terms of frequency and wavelength.¬†In vaccum , all types that emit electromagnetic waves, irrespective of wavelength, move in the exact same direction, i.e., 3.0 per 108 m s-1 (2.997925 in 108 ms-1 which is precise).¬†This is referred to as the speed of light, and is represented as a symbol called “c”.¬†It is the frequency (n ) and the wavelength (l) and speed of light (c) are linked through an equation (2.5).¬†C = n l other quantity that is commonly used, especially in spectroscopy is the number of waves ( ).¬†It is an amount of light wavelengths for each unit.¬†Its units are the reciprocal of wavelength units, i.e., m-1.¬†Best JEE Coaching Centre in Aizwal.¬†

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However , the most frequently used units is cm-1 (not SI unit).Particle Nature of Electromagnetic Radiation the Planck’s Quantum Theory Some of the experiments, like the phenomenon of diffraction* and interfering** are explained through the wave nature of electromagnetic radiation.¬†But, here are a few of the phenomena that can be explained without the help of the electromagentic theory from 19th century Physics (known as classical Physics): (i) the nature of radiation emission emanating from bodies that are hot (black radiation from bodies) (ii) the ejection of electrons off the metal surface as radiation hits its surface (photoelectric phenomenon) (iii) variation in temperature-dependent heat capacity of solids in relation to of temperature(iv) Line spectrums of atoms that have special references to hydrogen.¬†These phenomena suggest that the system can absorb energy only in discrete quantities.¬†Any energy that is possible are not absorbed or radiating.¬†Top JEE Coaching Centre in Aizwal.¬†

It is worth noting that the first scientific explanation for that black-body radiation discussed earlier was offered by Max Planck in 1900. We must first attempt to comprehend this phenomenon, that is described below The hot object emits electromagnetic radiations across a vast spectrum of wavelengths. When temperatures are high the majority of radiation occurs within the visible portion within the visible spectrum. When the temperature rises the proportion of shorter spectrum (blue radiation) is produced. For instance when iron rods are being heated by a furnace it begins to turn dull red, and then gets more and greater red, as temperature rises. When the rod is heated more the radiation that is emitted turns blue and then white when the temperature gets high. This means that the red radiation is the most intense at a certain temperature, while blue radiation is more intense at other temperatures. 

This implies that the intensity of various wavelengths of radiation produced by a hot object depend on the temperature.¬†In the late 1850’s, it was understood that objects made from different materials, and kept at various temperatures produce different levels of radiation.¬†Additionally when the surface of an object is exposed to radiation (electromagnetic radiation) there is a small amount of radiation energy is typically reflective, which means that the absorbed portion is then some of it is transferred.¬†The reason for this insufficient absorption is the fact that everyday objects are generally insufficient absorption of radiation.¬†A perfect body, one that emits and absorbs all frequencies of radiation in a uniform manner, is referred to as an “black body” and the radiation produced by such an object is referred to as”black body radiation.¬†In practice, no such body exists.¬†Carbon black is a good approximation to a black body.¬†A good physical analogy to the black body is a cavity that has one tiny hole that is the only opening.¬†Top JEE Coaching Centre in Aizwal.¬†

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The rays that enter the cavity is reflected off by the walls of the cavity, and eventually be absorbed by walls. A black body can also be an ideal radiator of radiation. Additionally, a body that is black is in equilibrium thermally with its surroundings. It emits the same amount of energy per square meter that it absorbs from its surroundings at any given moment. There is a certain amount that is emitted (intensity of the radiation) from a dark body as well as its spectrum distribution is dependent solely on the temperature. Best JEE Coaching Centre in Aizwal.  At a particular temperature, the intensity of radiation emitted rises with increase in wavelength. It then it reaches its maximum at a particular wavelength and then decreases as the wavelength increases as illustrated in Figure. 2.8. Additionally, as the temperature rises, the maximum of the curve changes to shorter wavelengths. Many attempts were made to estimate the intensity of radiation in relation to of the wavelength. 

However, the results from the previous experiment cannot be adequately explained by using the theory of light waves.¬†Max Planck arrived at an acceptable relationship through the assumption that absorption and emission of radiation originates from oscillators i.e. the atoms that are within the wall of the black bodies.¬†Their frequency of oscillation changes due to interaction with oscillators that emit electromagnetic energy.¬†Planck believed the radiation can be subdivided into discrete pieces of energy.¬†He proposed that molecules and atoms can release or absorb energy in small quantities, rather than in continuous fashion.¬†He gave the term quantum to the smallest amount of energy that could be released or absorbed by electromagnetic radiation.¬†It is believed that the energy (E ) of the quantum of radiation can be compared to the intensity (n ) as calculated through the equation (2.6).¬†E = Hu (2.6) the proportionality constant called ‘h’ is also known as Planck’s constant . It has the value of 6.626×10-34 J.

¬†Based on this theory, Planck was in a position to explain the pattern of intensity of radiation of the black bodies as a function of wavelength or frequency at various temperatures.¬†Quantisation can be similar to being on an escalator.¬†It is possible to stand on every step of the staircase, however it’s not possible to stand between two steps.¬†The energy may take any one of the numbers from the set below however it cannot be taken on any value between them.¬†E = 0 2, hu, 3hu ….nhu ….. Effect of the photoelectric The Effect in 1887 H. Hertz performed an extremely fascinating experiment where electrons (or electrical current) were released after certain metals (for example , potassium caesium, rubidium, and caesium.)¬†were exposed to light like in Fig.2.9.¬†This phenomenon is known as Photoelectric effect.¬†The results of this experiment wereas follows: (i) Electrons get ejected off the surface of the metal when the light beam is struck by the metal area, i.e., there is no time delay between the impact of the the light beam and the expulsion of electrons off the metal surface.¬†Best JEE Coaching Centre in Aizwal.¬†

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The amount of electrons released are proportional to brightness or intensity of light. (iii) For every metal there is a specific minimum frequency, n0 (also known as the threshold frequency) that is below which the effect of photoelectric is not noticed. If a frequency is greater than zero, the electrons that are ejected are released with a certain energetic energy. The energy of these electrons are increased with increasing frequency of the light source used. These results can be explained only on the foundation of the laws of classical physical science. According to this theory the energy quantity of the light beam is dependent on the intensity that the light emits. That is, the amount of electrons released and the their kinetic energy will depend on the intensity of light. Top JEE Coaching Centre in Aizwal. It has been found that, even though the quantity of electrons released does depend on the brightness of light but the kinetic energy produced by electrons that are ejected is not. 

For instance that bright red light (n equals (4.3 up to 4.6) 1014 Hz] at any intensity (intensity) could shine upon the surface of a piece made from potassium metal over a period of time and there is no photoelectrons released.¬†However, once even a small amount of blue glow (n = 5.1-5.2 1014 Hz) is shining on the metal of potassium and the photoelectric effect is seen.¬†A the threshold frequency (n 0) for potassium metal is 5.0×1014 Hz.¬†Einstein (1905) has been capable of explaining the photoelectric phenomenon using the quantum theory that Planck developed of electromagnetic radiation for a base.¬†The minimum energy needed to release electrons is hn0 (also known as work function W0 in Table 2.2) and the energy difference (hn + Hn0 ) is transferred to the power of the photoelectron.¬†In accordance with the principle of conservation of energy the kinetic energy of an discharged electron is determined in the form of equation 2.7.¬†(2.7) in which me represents the electron’s mass and v is the velocity that goes with the electron that was ejected.¬†

In addition, a stronger beam of light is composed of a more photons, therefore, the amount of electrons released is higher than when the beam with less intensity of light is utilized. Dual behavior in Electromagnetic Light The particle-like nature of light presented an issue for scientists. On the one hand light could be able to explain black-body radiation as well as the photoelectric effects in a way that was satisfactory, however on the contrary it did not agree with the observed wave-like behaviour of light that could account for the phenomenon of diffraction and interference. One way to solve the problem was to accept that light has both particle and wave-like properties i.e. it has dual behavior. Based on the results of the experiment we can conclude that light behaves either waves or as an emitted stream of particles. Top JEE Coaching Centre in Aizwal.  When radiation is in contact with matter, it exhibits properties that resemble particle as opposed to the wavelike properties (interference and diffracted) that it displays when it travels. 

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This idea was completely foreign to the way scientists saw radiation and matter, and it took them quite a while to convince themselves of the validity. As you will see in the future, that microscopic particles such as electrons display this duality of wave-particles. C:\Chemistry XI\Unit-2\Unit-2(2)-Lay-3(reprint).pmd 27.7.6, 16.10.6 (Reprint) Albert Einstein, a German born American physicist, is regarded by many as one of the two great physicists the world has known (the other is Isaac Newton). The three research papers he wrote (on particular relativity as well as Brownian motion as well as the effect of photoelectric) that were published in 1905 Albert Einstein (1879-1955) while employed as an assistant to the technical department at the Swiss patent office located in Berne has profoundly influenced the evolution of Physics. He was awarded the Nobel Prize in Physics in 1921 for his research into photoelectric effects. Top JEE Coaching in Aizwal. A beam of light shining onto the surface of a metallic object could, therefore, be thought of as shooting a stream of particles, called photons. 

If a light particle with enough energy hits an electron within the metal’s atom the energy is transferred immediately to the electron in the collision. The electron is ejected with no delay or time-lag.¬†The greater the energy produced by the photon, more is the transfer of energy to the electron, and higher the energetic energy of the released electron.¬†In other words, the kinetic energy released by the electron corresponds to the frequency electromagnetic radiation.¬†Because the photon that is struck has an energy that is equal to hn and the2.3.3 evidence for quantizationElectronic Energy Levels Atomic spectrums Light’s speed varies on the nature of the medium that it travels.¬†In the end, the light beam gets altered or diverted from its path as it travels through different mediums.¬†It is evident that when white light is passing through a prism the wavelength with a shorter wavelength is more bent than one with a higher wavelength.¬†Because normal white light is composed of waves of all wavelengths of the visible spectrum the white light is divided into a range of colored bands, referred to as spectrum.¬†

The red light with the longest wavelength most deviated, while violet light with the short wavelength, is skewed the most.¬†Its white spectrum which we can observe can be seen as ranging in wavelength from violet 7.50 1014 Hz up and red with 4x1014Hz.¬†The spectrum we see is known as continuous spectrum.¬†Continuous as violet blends with blue, blue transforms into green, and then on.¬†Similar spectrums are created when a rainbow is formed on the sky.¬†Keep in mind that visible light only represents one small part of electromagnetic radiation (Fig.2.7).¬†When electromagnetic radiation is in contact with matter, molecules and atoms, they might absorb energy, and eventually reach to a higher energy level.¬†At higher energy levels, they are unstable.¬†In order to return back to their regular (more stable state, with lower energy) state of energy, molecules and atoms emit radiation across electromagnetic spectrum.¬†Emission and Absorption Spectrums A spectrum of electromagnetic radiation produced by a substance which has taken in energy is known as”emission spectrum.¬†Ions, molecules, or particles that absorb radiation are referred to as “excited”.¬†Top JEE Coaching in Aizwal.¬†

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In order to create the emission spectrum transferred to the sample by heating or radiating it, as well as the frequency (or frequency) of the radiation that is emitted by the sample, when it gives the energy absorbed is recorded.¬†Absorption spectrums are the negative image that is an emission spectrum.¬†A continuous spectrum of radiation is transmitted through a substance that absorbs certain wavelengths of radiation.¬†The wavelength that is not present, which corresponds to radiation absorption by material, leaves dark spaces in the bright spectrum.¬†The study of absorption or emission spectrums is called spectroscopy.¬†The spectrum of visible spectrum, which we have described previously, was continuous since every wavelength (red from violet) of visible light are depicted in the spectrum.¬†The emission spectra for atoms in gases, on contrary, don’t have a continuous range of wavelengths ranging from violet to red but rather emit light at certain wavelengths, with dark spaces in between the wavelengths.¬†Top JEE Coaching in Aizwal.¬†

They are also known as line spectra, also known as atomic spectra because the radiation emitted is distinguished through the presence of lines that are bright within the spectrum (Fig. 2.10 pages 45 and 2.10). The spectra of line emission are of major importance when studying electronic structure. Every element has its own unique line emission spectrum. The distinct lines that appear in the atomic spectrum are utilized for chemical analysis to find unknown elements in the same manner fingerprints are used to identify individuals. The exact alignment of the lines in the emission spectrum of elements of an element that are known with lines of an unidentified sample is quick to establish who is the former, German chemist, Robert Bunsen (1811-1899) was one of the pioneers to make use of line spectra in order to determine the elements. The elements like rubidium (Rb) and caesium (Cs) Thallium (Tl) (Cs), indium (In) and gallium (Ga) and scandium (Sc) were discovered by analysing their minerals using spectroscopic techniques. 

Helium (He) has been discovered on the Sun using a using spectroscopic methods.¬†Line The Spectrum of Hydrogen A electrical discharge is transmitted through hydrogen gas, the H2 molecules break up and the excitation of hydrogen atoms produces electromagnetic radiation with different frequency.¬†The spectrum of hydrogen is composed of various lines that are named in honor of their creators.¬†Balmer discovered in 1885 on the foundation of his observations lines are described as wavenumber ( ) and the visible lines of the spectrum follow the formula. (2.8) in which n represents an amount that is equal at or higher than (i.e. 3,4,5). 3,4,5 ,….) The group of lines outlined by this formula is known as”the” Balmer series.¬†Balmer’s Balmer line series is the sole ones that are visible in the hydrogen spectrum. appear in the visible portion within the electromagnetic spectrum.¬†The Swedish spectroscopist Johannes Rydberg, noted that all lines of the hydrogen spectrum can be described using the expression : (2.9) where n1=1,2 …….. n2 = n1 + 1. 2. ……¬†The figure of 109,677cm-1 is known as”the Rydberg constant of hydrogen.Top JEE Coaching in Aizwal.¬†

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The initial five series of lines which correspond to n1 = 1 2 3 5, 4 are referred to as the Lyman, Balmer, Paschen, Bracket and Pfund series according to Table 2.3 depicts these five sequences of transitions within the spectrum of hydrogen. Figure 2.11 (page 46) depicts how to identify the Lyman, Balmer and Paschen series of transitions for the hydrogen atom. Of all elements, hydrogen atom is the one with the most simple line spectrum. Line spectrum gets complex when you are dealing with heavier atoms. However, there are some features that have commonality to all line spectrums, i.e., (i) the spectrum of an the element is unique, in its own way and (ii) it is consistency in the spectrum of every element. Top JEE Coaching in Aizwal. The main questions that come up are what are the causes of these similarities? Do they have something to do in the electron structure the atoms? These are the questions that need to be addressed. In the future, we will see how the solutions to those questions are the foundation for understanding the how electronic elements work. 

BOHR’S MODEL for HYDROGEN ATOM Neils Bohr (1913) was the first person to describe quantitatively the basic aspects of the hydrogen atoms and their spectrum.¬†He based his theory on Planck’s the quantisation of energy.¬†Although the theory isn’t the current quantum mechanics but it could still be applied to figure.¬†2.11 Transitions of electrons inside the hydrogen atom (The diagram illustrates three series of transitions: Lyman, Balmer and Paschen sequence of transitions) clarify a number of aspects in the structure of the atom and the spectra.¬†Bohr’s hydrogen atom model is built on the following postulates that: i) The electron inside the hydrogen atom moves around the nucleus along the form of a circular path with defined radius, energy and.¬†These paths are referred to as orbits stationary states or permitted energy states.¬†The orbits are placed in a symmetrical manner within the nucleus.¬†II) The energy of an electron within the orbit is not affected in the length of.¬†

But, it will shift from a stationary state to a more stationary state if the necessary amounts of energy are taken up by the electron or energy is released as the electrons move from a stationary state to a lower stationary state (equation 2.16).¬†The change in energy is not in a continuous fashion.¬†An angular Momentum Similar to linear momentum which is the result of the mass (m) as well as linear velocity (v) and angular momentum is the result of the Moment of Inertia (I) and the angular velocity (o).¬†If an electron is mass me , traveling in the form of a circle with a radius of r around the nucleus the angular momentum is I x o . Since I is me and r2 with o being v/r, where the linear velocity is v me, and angular momentum = me r2 me vr II) A frequency that is absorbed or released in the event of a transition in two states, which differ in energy due to E is calculated as follows the formula: n = – H E E h 1 (2.10) In which E1 and E2 represent the energy levels of the higher and lower allowed energy states.¬†This expression is often referred to as Bohr’s Frequency Rule.¬†IV) The energy of an electron is quantified.¬†Top JEE Coaching in Aizwal.¬†

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In which me is the electron’s mass me, v is the velocity and the radius is the orbit through the electron’s orbit.¬†So, an electron is able to only move in orbits in which its angular velocity is integral multiplied by the ratio of h/2p.¬†This means that angular momentum is quantified.¬†Radiation can be emitted or destroyed only when the electron’s transition is made from one quantised amount of the angular momentum to another.¬†Thus Maxwell’s electromagnetic theory can not apply in this case, which is the reason there are only certain orbits fixed are permitted.¬†The particulars regarding the calculation of the energies for the stationary state utilized by Bohr are very complicated and will be covered in more advanced classes.¬†According to Bohr’s theory of hydrogen atoms the following formula is applicable:) the stationary state of electrons are identified as 1 to 3. ……….¬†This integral numbers (Section 2.6.2) can be referred to as the Principal Quantum Numbers.¬†b) The radii of stationary states are represented as (rn = n2 a0 (2.12) where A0 = 52.9 pm.¬†Therefore, the distance of the first state stationary, known as the Bohr orbit can be calculated as 52.9 pm.¬†Typically, the electron in the hydrogen atom can be found on the Bohr orbit (that is the n=1).¬†If n is increased, its value, the measure of r will rise.¬†Top JEE Coaching in Aizwal.¬†

Also, the electron will remain away in the nucleus.¬†The electron is present in the nucleus.) The most important characteristic that is associated with electrons is the energy that it has in it’s stationary condition.¬†It is expressed through the phrase.¬†.¬†This diagram is known as the energy-level diagram.¬†If an electron is free in the absence of the nucleus it is regarded as zero.¬†In this scenario, the electron is in its stationary condition of Principal Quantum number = n = and is known as an ionized hydrogen atom.¬†If the electron is pulled by the nucleus, and is found in orbit n the energy is released. What is”negative energy in electronics” (En) for the hydrogen atom refer to?¬†The electron’s energy within a hydrogen atom bears negative signs for all orbits that could be possible (eq.¬†2.13).¬†What is this symbol convey?¬†The negative sign signifies that the electron’s energy inside the atom is lower than that of an electron that is free at rest.¬†Free electrons at rest is infinitely separated from the nucleus, and is assigned an Energy value zero.¬†Mathematically speaking, this is equivalent to setting n to be equal to infinity according to this equation (2.13) which means that E = 0.

As the electron moves close to its nucleus (as the radius of n diminishes), En becomes larger in absolute terms and becomes becoming more and more negative.¬†The energy that is the most negative is n=1, which corresponds to the stable orbit.¬†We refer to this as”the state of the earth.¬†Niels Bohr (1885-1962) Niels Bohr was a Danish scientist, received the Ph.D. in physics from the University of Copenhagen in 1911.¬†The following year, he worked in the company of J.J. Thomson and Ernest Rutherford in England.¬†Then, in 1913, the pair retreated to Copenhagen where continued to reside for the rest of his existence.¬†In 1920, he was appointed director of the Institute of theoretical Physics.¬†After the First World War, Bohr worked hard to promote peaceful uses of nuclear energy.¬†He was awarded the initial Atoms for Peace award in 1957.¬†Bohr was given his Nobel Prize in Physics in 1922.¬†2022-23, 48 CHEMISTRY and its energy is decreased.¬†This is why you see the the negative symbol in the equation (2.13) and shows its stability with respect to zero-energy reference. that n = .Bohr’s theory could also be applied to ions that contain just one electron, similar to the hydrogen atom.¬†For instance, He+ Li2+ Be3+, He+ Li2+ and the list goes on.¬†Top JEE Coaching in Aizwal.¬†

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The energy of stationary states that are associated with these types of Ions (also called hydrogen like species) are outlined in the term.¬†This implies that the electrons are strongly attached with the nucleus.¬†It is also possible to calculate the velocities of electrons.) There is also the possibility to determine the speed of electrons through these orbits.¬†While the exact formula isn’t provided here, the qualitative magnitude of the velocity of electrons increases with increasing positive charge in the nucleus. It decreases with the increase in primary quantum number.¬†2.4.1 Explaination of Line Spectrum of Hydrogen Line spectrum that is observed in the the case of hydrogen atoms, as explained in section 2.3.3 and 2.3.3, can be explained in a quantitative manner by using Bohr’s model.¬†According to the assumption 2 the radiation (energy) can be absorbed when the electron is moved between the orbits of a the smaller Principal quantum number and then to orbit with a a higher Principal quantum number. In contrast, energy (energy) is released when the electron is moved from a the higher orbit to the lower orbit.

In the case an absorption spectrum, the nf is greater than Ni and the expression in parenthesis is positive, and energy is absorption.¬†In contrast, in the cases of emission spectrum, the ni value is greater than nf, so E is negative, and the energy released.¬†The formula (2.17) is identical to the one used by Rydberg (2.9) which was derived by using experimental data at the time.¬†Additionally, every spectrum line, whether it is in emission or absorption spectrums could be linked to a specific transition in the hydrogen atoms.¬†If there is a large amount of hydrogen atoms possible transitions are visible and result in a huge numbers of spectrum lines.¬†The intensity or brightness of spectral lines is dependent on the amount of light particles of same wavelength or frequency that are absorbed or released.¬†Constraints of Bohr’s Model Bohr’s theory of hydrogen’s atom was in no doubt a step up from Rutherford’s nuclear model as it could explain the line spectra and stability of hydrogen atoms and hydrogen-like ions (for instance, He+, Li2+, Be3+ and the list goes on).¬†But, the model of Bohr was too simplistic to take into account the following aspects.¬†I) It is unable to consider the more intricate specifics (doublet which is a pair of closely spaced lines) of the hydrogen atom spectrum that can be observed through sophisticated spectroscopic methods.¬†

The model also fails understand the spectrum observed by other atoms than hydrogen, like the helium atom, which has just two electrons.¬†In addition, Bohr’s theories were not able to explain the split of spectral lines when in presence of magnetic fields (Zeeman Effect) and electric fields (Stark Effect).¬†II) It did not provide a reason for the capacity of atoms make molecules using chemical bonds.¬†That is considering the above points it is necessary to develop a more comprehensive theory to clarify the most important characteristics that characterize the complex structure.¬†2.5 Towards QUANTUM MECHANICAL MODEL of the ATOM With regard to the shortcomings of Bohr’s model, efforts were made to formulate an appropriate and more general model of the atoms.¬†Two key developments that helped to the development of this model were: 1.¬†Dual behavior of matter 2.¬†Heisenberg uncertainty principle.¬†2.5.1 Dual Behavior of Matter French scientist, physicist de Broglie, in 1924 suggested that matter, just like radiation, could also show dual behavior i.e. it should exhibit particles and wavelike properties.¬†This implies that, similar to the way that a photon has momentum and wavelength, electrons also exhibit momentum in addition to wavelength, de Broglie, from this analogy, proposed the following equation for length (l) and the momentum (p) of the particle of material.

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2.5.2 The Heisenberg Uncertainty Principle Werner Heisenberg a German physicist in 1927, proposed the uncertainty principle, which is the result of the two different properties of radiation and matter.¬†It declares that it is impossible to know simultaneously the precise location and velocity (or speed) for an electron.¬†Mathematically, this can be expressed as follows: the equation (2.23).¬†L= = h m, h v (2.22) (2.22) in which m represents the weight of the particle and v is its velocity and p its speed.¬†De Broglie’s prediction was proved by experiments when it was discovered that an electron beam experiences diffracted light, which is a typical of waves.¬†This information can be utilized to create an electron microscope. It is based on the wave-like conductivity of electrons in the same way that normal microscopes make use of the wave-like characteristics of light.¬†The electron microscope is a potent instrument for modern research due to its magnification of around 15 million.¬†It is important to note that according to de broglie each object that is in motion has a wave-like character.¬†The wavelengths of ordinary objects are so small (because of their massive mass) they have no wave characteristics are not detectable.¬†The wavelengths of electrons and various subatomic particles (with tiny mass) are however detectable experimentally. Top Coaching centre for JEE in Aizwal.

Results from the following questions confirm these assertions qualitatively.¬†Problem 2.12 What is the length of a ball with a mass of 0.1 kg that is moving at the speed of 10 meters 1 s-1 ?¬†Louis de Broglie (1892 – 1987) Louis de Broglie, the French scientist, was a physicist who studied history as a student in the early 1910’s.¬†His passion for science grew because of his radio communications assignment during World War I.¬†He graduated with a Dr. Sc.¬†at the University of Paris in 1924.¬†He was a professor of theoretical Physics in The University of Paris from 1932 until his retirement in 1962.¬†The award was Nobel Prize in Physics Nobel Prize in Physics in 1929¬†where x represents the uncertainty of position and (2.23) where px (or the value vx) represents the uncertainties in the momentum (or the velocity) that the particle.¬†If the location of the electron is determined with great precision (x is low) (2.23) then the speed of the electron is undetermined [(vx ) is high(2.23).¬†However in the event that the velocity of the electron can be determined accurately ((vx ) is low) which means that the location of the electron is unclear (x will be huge).¬†So, if you conduct physical measurements of the electron’s velocity or position it will reveal a blurred or fuzzy image.¬†The principle of uncertainty can be best understood through the use of an illustration.¬†

If you were asked to measure the thickness the paper using an unmarked, un-marked metrestick.¬†It is obvious that the results are extremely inconclusive and insignificant. To be able to achieve any precision, you must make use of an instrument that is graduated in units less that the size of the sheet of paper.¬†Similar to this, to determine the exact location the electron’s position, you must employ a meterstick calibrated to units less than the dimensions of an the electron (keep remember that electrons are thought of as a point-charge and therefore is not in no way dimensionless).¬†To study an electron, we could shine it by using “light” as well as electromagnetic radiation.¬†The “light” that is used has to be shorter in wavelength than the size of the electron.¬†The high-energy photons of these light sources.¬†The electron’s energy through collisions.¬†Through this process, we surely could determine the location of the electron. However, we’d have no idea about the speed of the electron following the collision.¬†The significance of the uncertainty Principle A number of major effects of the Heisenberg Principle can be that it blocks the existence of certain routes or trajectories for electrons as well as other particles similar to them.¬†Top Coaching centre for JEE in Aizwal.

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The course that an object follows is determined by the position and velocity over a variety of moments.¬†We know the location an object is at any given moment and also know its speed and the forces that are acting upon it at that moment it is possible to determine what the position of the body will be a few minutes later.¬†This means that the location of the object and its velocity define its course.¬†Because for subatomic objects like an electron it is not possible to establish the position and velocity at any moment to an indefinite level of precision It is therefore not possible to discuss the trajectory for an electron.¬†The impact of the Heisenberg’s Uncertainty Principle is only relevant when it comes to motion of microscopic objects, and is insignificant for macro-sized objects.¬†This is evident from these examples.¬†When the uncertainty principle applies to an object that is weight, for instance, 10-6 kg, then (10-6 kg) and it is Werner Heisenberg (1901 – 1976) Werner Heisenberg (1901 – 1976) earned the Ph.D. from physics at the University of Munich in 1923.¬†He spent the next time working alongside Max Born at Gottingen and three years working with Niels Bohr, in Copenhagen.¬†He was a professor of Physics in the University of Leipzig from 1927 until 1941.¬†In World War II, Heisenberg was responsible for German research into the nuclear bomb.¬†Top Coaching centre for JEE in Aizwal.

Following the war, he was appointed director of the Max Planck Institute for physics in Gottingen.¬†He was also an accomplished climber.¬†Heisenberg received his Nobel Prize in Physics in 1932.¬†2022-23 52 CHEMISTRY of vx derived is extremely tiny and not significant.¬†Thus, it is possible to claim that when dealing with large or heavy objects, the uncertainties have no significant consequence.¬†For the microscopic nature of an electron, on the other side.¬†v.x calculated is significantly larger and the uncertainties that result are of significance that is such that the traditional representation of electrons moving through Bohr’s orbits (fixed) is not able to hold.¬†Therefore, it implies that the precise assertions of the momentum and position of electrons must be replaced with probabilities that the electron is an exact place and speed.¬†This is the case when you use the quantum mechanical models for atoms.¬†= 0.579×107 M s-1 (1J equals 1 kg/m2 2) = 5.79×106 meters per second 2.16 Golf ball weighs an approximate weight of 40g and it has a speed of 45m/s.¬†If the speed is determined with a precision that is 2% or more, then calculate the degree of uncertainty in the direction of the ball.¬†Solution The uncertainty of the rate is 22% i.e. applying this formula (2.22) = 1.46×10-33 m.¬†

This is almost 1018 times smaller than the diameter of an average nuclear nucleus.¬†Like we said earlier, for big particles the uncertainty principle puts an undefined limit on the accuracy of measurements.¬†The reasons for the failure of the Bohr Model We can now be aware of the causes for the deficiency that is Bohr model. Bohr model.¬†In the Bohr model, the electron is considered to be charged particles moving within well-defined circular orbits around the nucleus.¬†The characteristic of a wave in electrons is not thought of in the Bohr model.¬†Additionally an orbit is clearly defined path , and it can be completely determined only if the speed and position that the electron travels at are determined precisely simultaneously.¬†This isn’t possible under the Heisenberg uncertainty principle.¬†Bohr models of the hydrogen atom thus, does not just ignore the dual nature of matter however, it also violates the Heisenberg principles of uncertainty.¬†Based on the problem 2.15 A microscope using suitable photons is used to find the electron within an atom with the range that is 0.1 A.¬†What is the degree of uncertainty when measuring its velocity?Top Coaching centre for JEE in Aizwal.¬†OF ATOM 53 Considering the inherent flaws of the Bohr model It was not a good idea in expanding the Bohr models to different atoms.¬†

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In reality, an understanding of how the structures of the atoms work was necessary that could explain the duality of matter between wave particles and conform to the Heisenberg the uncertainty theory.¬†This was realized with the development the quantum theory of mechanics.¬†2.6 QuantumMechanical Model of ATOM Classical mechanics that is built on Newton’s laws for motion, is able to describe what happens to macroscopically-sized objects like falling stones and orbiting planets. These have an atomic-like behavior as demonstrated in the earlier section.¬†However, it is not applicable to microscopic objects, such as molecules, electrons, atoms as well as other molecules.¬†This is due to the nature of classical mechanics that ignores the dual nature of matter, particularly for subatomic particles as well as the principle of uncertainty.¬†The science field that considers the dual nature of matter is known as quantum mechanics.¬†Quantum mechanics can be described as a theoretic science that is concerned with studying the movements of microscopic objects with the ability to observe wave-like and particle-like properties.¬†It outlines the rules of motion these objects follow.¬†If quantum mechanics are applied to macro-sized objects (for that wave-like properties are not significant) its results will be similar to those of classical mechanics.¬†

Quantum mechanics was invented independent of 1926, in 1926 by Werner Heisenberg and Erwin Schrodinger.¬†In this article, we will be discussing quantum mechanics built on the concepts that wave motion is a concept.¬†The quantum equation that is the basis that is quantum mechanics created by Schrodinger and was awarded the Nobel Prize in Physics in 1933.¬†The equation that incorporates the the waveparticle duality of matter suggested by de Broglie is quite complex and higher mathematical knowledge is necessary to figure it out.¬†It is possible to learn the solutions for different systems within higher levels.¬†For an entire systems (such like an atom, or molecules which’s energy is not altered over time) the Schrodinger equation can be expressed as follows: where is an operator in mathematics called Hamiltonian.¬†Schrodinger provided a method of formulating this operator from the expression of the energy total of the system.¬†This equation calculates the total energy that the system has. It includes the energy kinetics of all subatomic particles (electrons and nuclei) as well as the attractive potential that exists between nuclei and electrons and repulsive power between nuclei and electrons individually.¬†The solution to this equation is an equation for E, and the an ps.¬†Top Coaching centre for JEE in Aizwal.

Hydrogen Atom and the Schrodinger Equation If the Schrodinger equations are solved in relation to the hydrogen atom it is possible to determine the energy levels that electrons can be occupying and the associated the wave function(s) (ps) that the electron has that is associated with each level of energy.¬†Quantized energy states as well as their associated wave functions, which are defined by three quantum numbers (principal quantum number n and azimuthal quantum number l, and magnetic quantum number ml ) are an obvious consequence of the solution to Schrodinger equation. Schrodinger equation.¬†When an electron is Erwin Schrodinger (1887-1961) Erwin Schrodinger was the Austrian scientist, received the Ph.D. in the field of theoretical physics at the University of Vienna in 1910.¬†In 1927, Schrodinger was appointed to succeed Max Planck at the University of Berlin upon the request of Planck.¬†After 1933 Schrodinger was forced to leave Berlin for reasons of disapproval against Hitler as well as Nazi policies. He went back in Austria following the war in.¬†Top Coaching centre for JEE in Aizwal.¬†Following Germany’s invasion of Austria in the hands of Germany, Schrodinger was forcibly removed from his post as a professor.¬†