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Dual Nature Of Radiation Class 12 Physics Notes

Published in: IIT JEE Mains | Physics
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dual nature of radiation class 12 physics notes ncert

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    Physics Notes by Akhil. Dual Nature of Radiation and Matter (chapter 11) Cathode Rays Cathode rays are the stream of fast moving electrons. These rays are produced in a discharge tube at a pressure below 0.01 rom of mercury. Properties of Cathode Rays (i) Cathode rays are not electromagnetic rays. (ii) Cathode rays are deflected by electric field and magnetic field. (iii) Cathode rays produce heat in metals when they fall on them. Specific charge of cathode rays means ratio of charge and mass. Specific charge of electron was determined by J J Thomson .Specific charge of electron = (e / m) . The value of specific charge of an electron is 1.7589 * 1011 C / kg. Millikan measured the charge of an electron through his popular oil drop experiment. The charge of the electron as determined by Millikan was found to be 1.602 * 10-19 C. Electron Emission It is the phenomenon of emission of electron from the surface of a metal. Electron emission can obtained from the following process (i) Thermionic — By suitable heating, provide sufficient thermal energy. (ii) Photoelectric emission - When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surface. These photo(light)-generated electrons are called photoelectrons. (iii) Field emission - By applying a very strong electric field to a metal. Photoelectric Effect The phenomena of emission of electrons from a metal surface, when radiations of suitable frequency is incident on it, is called photoelectric effect. Terms Related to Photoelectric Effect v/ Work Function( (PO) The minimum amount of energy required to eject one electron from a metal surface, is called its work function. v/ Threshold Frequency (Do) The minimum frequency of light which can eject photo electron from a metal surface is called threshold frequency of that metal. Threshold Wavelength (Xmax) The maximum wavelength of light which can eject photo electron from a metal surface is called threshold wavelength of that metal. • Relation between work function, threshold frequency and threshold wavelength (PO = hU0 = (hc / Xmax ) Laws of Photoelectric Effect - (Basic features) I . For a given metal and frequency of incident light, the photo electric current ( rate of emission of photoelectrons) is directly proportional to the intensity of incident light. Means number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation. 2. For a given metal, there is a certain minimum frequency, called threshold frequency, below which there is no emission of photoelectrons takes place. 3. For above threshold frequency, the maximum kinetic energy of photoelectrons depends upon the frequency of incident light. 4. The photoelectric emission is an instantaneous process. Effect of potential on photoelectric current- v/ Saturation current- Maximum value of the photoelectric current is called saturation current. v/ Stopping Potential (Vo). The minimum negative potential at which photoelectric current becomes zero. v/ Maximum kinetic energy of photo electrons (K.E.)max = ( h) mv2max = e. Vo
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    v/ For a given frequency of the incident radiation, the stopping potential is independent of its intensity. Means maximum kinetic energy of photoelectrons depends on the light source and the emitter plate material, but is independent of intensity of incident radiation. Effect of frequency of incident radiation on stopping potential — • greater the frequency of incident light, greater is the maximum kinetic energy of the photoelectrons. • there exists certain minimum cut-off (threshold) frequency vo for which stopping potential is zero. • maximum kinetic energy of the photoelectrons and stopping potential VO varies linearly with the frequency of incident radiation, but is independent of its intensity. frequency v of incident radiation, lower than threshold frequency (vo ) , no photoelectric emission is possible even if the intensity is large. For a given photosensitive material & frequency ( U > ) of incident radiation - photoelectric current is directly proportional to intensity of incident light. Stopping potential or equivalent maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of its intensity. PHOTOELECTRIC EFFECT AND WAVE THEORY OF LIGHT Phenomena of interference, diffraction and polarization explained in a natural and satisfactory way by the wave picture of light— light is an electromagnetic wave consisting of electric and magnetic fields with continuous distribution of energy over the region of space over which the wave is extended. Wave theory is unable to explain the most basic features of photoelectric emission ? According to the wave theory of light, the free electrons at the surface of the metal absorb the radiant energy continuously, when beam of radiation falls on it. So greater the intensity of radiation, the greater are the amplitude of electric and magnetic fields. Greater the intensity, the greater should be the energy absorbed by each electron. maximum kinetic energy of the photoelectrons is then expected to increase with increase in intensity. So it's not depend on frequency of radiation. So threshold frequency does not exist in wave theory. So it contradict with basic feature of photoelectric emission. Photoelectric emission is instantaneous process. But in the wave picture, the absorption of energy by electron takes place continuously over the entire wavefront of the radiation. Energy absorbed per electron per unit time turns out to be small. So it take much time to absorb sufficient energy to come from surface, so it contradict that photoelectric process is instantaneous process. EINSTEIN'S PHOTOELECTRIC EQUATION : ENERGY QUANTUM OF RADIATION— Einstein proposed a radically new theory of electromagnetic radiation to explain photoelectric effect. Radiation energy is buildup of discrete units called quanta of energy of radiation. Each quantum of radiant energy has energy = hU, where h is Planck's constant and U is the frequency of light. v/ If radiation absorbed by photoelectron having quantum of radiation energy ho exceeding the work function then then photoelectron come out with maximum kinetic energy v/ hU - (PO this equation called as Einstein's photoelectric equation. Observation from equation- Kmax depends linearly on frequency U , and is independent of intensity of radiation Kmax must be positive, implies that photoelectric emission is possible only if hU > (PO or U > where = Threshold frequency is directly proportional to work function. In this picture, intensity of radiation is proportional to number of energy quanta per unit area per unit time. so greater the number of energy quanta available, the greater is the number of electrons absorbing the energy quanta and therefore , greater number of electrons coming out of the metal (for v > vo). This explains why, for v > vo, photoelectric current is proportional to intensity.
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    In Einstein's picture, basic elementary process (absorption of a light quantum by a single electron) involved in photoelectric effect. This process is instantaneous. Thus, whatever may be intensity (the number of quanta of radiation per unit area per unit time) photoelectric emission is instantaneous. Intensity only determines how many electrons are able to participate in elementary process means photoelectric current. photoelectric equation Kmax = evo Kmax = hU- (PO evo = ho- (PO h 90 Vo = ( hU- (PO ) / e = This gives straight line graph with slope = (h/e), independent of the nature of the material. Millikan proved the validity of Einstein's photoelectric equation. PARTICLE NATURE OF LIGHT: THE PHOTON Photons are quantized energy particles. Photons are the packets of energy emitted by a source of radiation v/ rest mass of a photon is zero. v/ energy of each photon is E = hu Where h is Planck's constant and U is frequency of radiation. v/ The momentum of a photon p = ho / c = h/ v/ kinetic mass of photon v/ Photons are electrically neutral. A body can radiate or absorb energy in whose number multiples of a quantum ho, 2hU, 3hU . integer. WAVE NATURE OF MATTER- nhU, where n is positive wave nature of light shows up in the phenomena of interference, diffraction and polarization. photoelectric effect and Compton effect which involve energy and momentum transfer explained by particle nature of light. moving particles of matter should display wave-like properties under suitable conditions. If radiation shows dual aspects, so should matter. De Broglie proposed that the wave length 1 associated with a particle of momentum p is given as h wave length 1 = h/p = equation called de Broglie relation . wavelength called 'de Broglie wavelength mv the mass of the particle and v its speed. hv For photon: momentum p=energy /speed of light = c 1 hence proved - photon satisfy de Broglie relation v/ is smaller for a heavier particle (large m ) or more energetic particle (large v). m is An electron (mass m, charge e) accelerated from rest through a potential V. kinetic energy K of the electron equals the work done (e V) on it by the electric field: 2 K= - mv 2 h h 1 p2 2m
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    now put value of h, m , e 1.227 nm , where V is potential in volts. Heisenberg's uncertainty principle.- It is not possible to measure both the position and momentum of an electron (or any other particle) at the same time exactly. There is always some uncertainty (Ax) in the specification of position and some uncertainty (AP) in the specification of momentum. h Ax.Ap 211 Ax goes to zero then, (AP) must be infinite in order , and vice verca. Born's probability interpretation this means that the electron is not localised in any finite region of space. That is, its position uncertainty is infinite (Ax T), which is consistent with the uncertainty principle. DAVISSON AND GERMER EXPERIMENT- wave nature of electrons was first experimentally verified by Davisson and Germer in 1927 and independently by Thomson, in 1928, who observed diffraction effects with beams of electrons scattered by crystals. apparatus is enclosed in an evacuated chamber. It consists of an electron gun which comprises of a tungsten filament F, coated with barium oxide and heated by a low voltage power supply (L.T. or battery). Electrons emitted by the filament are accelerated to a desired velocity by applying suitable potential from a high voltage power supply (H.T. or battery). They made to pass through a cylinder with fine holes along its axis, producing a fine beam. The beam is made to fall on the surface of a nickel crystal. The electrons are scattered in all directions by the atoms of the crystal . The intensity of electron beam is measured by electron detector (collector). The detector is connected to a sensitive galvanometer, which records the current. The deflection of the galvanometer is proportional to intensity of electron beam entering the collector. By moving the detector on the circular scale at different positions, the intensity of the scattered electron beam is measured for different angle of scattering 0 ( the angle between the incident and the scattered electron beams). variation of intensity (I) of the scattered electrons with the angle of scattering 0 is obtained for different accelerating voltages. strong peak appeared in the intensity (I) of the scattered electron for an accelarating voltage of 54V at a scattering angle 0 = 500. From the electron diffraction measurements, the wavelength of matter waves was found to be 0.165 nm 1 227 V =54 volts , 1 0.167 nm Davisson Germer experiment confirms the wave nature of electrons and the de Broglie relation.

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