## dual nature of radiation

These are the main arguments we are going to discuss in this chapter notes. The energy (E1) of a radio photon is very less, but the number of photons (n) emitted per second in a radio wave is very large. 25.An electron microscope uses electrons accelerated by a voltage of 50 kV. CBSE Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter Notes in PDF are available for free download in myCBSEguide mobile app. The above three inconsistencies showed that wave theory of light could not explain the experimentally observed characteristics of photoelectric effect. (b) From your answer to (a), guess what order of accelerating voltage (for electrons) is required in such a tube? An  and a proton are accelerated from rest through same potential difference V. find the ratio of de–broglie wavelength associated with them? As per the wave theory, the maximum kinetic energy of the photoelectron should be affected by the change in intensity. Give reason for your answer? Average energy of a gas at temperature T, is given as: Mean separation between two atoms of the gas is given by the relation: Hence, the mean separation between the atoms is much greater than the de Broglie wavelength. ], Mean separation between two electrons, r=. The kinetic energy of the neutron is given by the relation: De-Broglie wavelength of the neutron is given as: It is clear that wavelength is inversely proportional to the square root of mass. In aluminum 4.2 eV are required to remove an electron. It intersects the at Hz, which is the threshold frequency  of the material. The wavelength associated with an electron will be: Kinetic energy K = (1/2)mv2 = (mv)2/(2m) = p2/2m. Kinetic energy (K) and velocity (v) are related as: De Broglie wavelength  and velocity (v) are related as: Using equation (2) in equation (1), we get: Hence, the kinetic energy of the neutron is J or eV. The maximum wavelength change possible in Compton effect is 0.05Å. The photoelectric effect proves the particle nature of radiation. The photoelectric effect takes place only when photons strike bound electrons because for free electrons energy and momentum conservations do not hold together. (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be? Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature and 1 atm pressure; and compare it with the mean separation between two atoms under these conditions. The total energy per unit for n falling photons is given as: The energy per unit area per second is the intensity of light. In the above formula, the expression for energy can only be used in the non-relativistic limit, i.e., for v << c. When very high speeds are concerned, the relativistic domain comes into consideration. This effect cannot be explained by classical theory (by wave nature of light). Total number of photons may or may not be constant. Dual Nature of Radiation and Matter; 1 (current) 2; 3; 4; The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is (a) h m k T (b) h 3 m k T If not, in what way is it modified? The beam traces a circular path of radius, r. It is the magnetic field, due to its bending nature, that provides the centripetal force for the beam. Wavelength of the radiation emitted from an iron source,  = 427.2 nm. Lect 01: Photoelectric Effect-01. Case-3-When the variation of photoelectric current was plotted against the potential for 3 different values of intensity of incident light (keeping the frequency constant). μ = cZ. In an experiment of photoelectric effect, the intensity () was doubled. 10. At a pressure 0.01 mm. Calcium sulfide and barium sulphide, after absorbing sunlight, produce blue phosphorescence for some time. 2. Ans. And while interacting with matter, it behaves as a particle, Photons of similar frequencies possess equal energies and equal momentums, Photons are electrically neutral (not having a net positive or negative charge). Fluorescent materials emit light only so long as light is incident on them. Position yourself for success with a comprehensive curriculum and guidance from seasoned mentors. (iii) Photoelectric current is directly proportional to the intensity of incident radiations, provided the given frequency is greater than the threshold frequency. When an electron is accelerated through a potential difference V then the energy acquired by electron, When these high energy electrons fall on target T of high atomic number, then X-rays are produced, whose wavelength is given by, The shortest wavelength of X-rays emitted is. Analyze quantum ideas at the nanoscale. (b) De Broglie wavelength of an electron accelerating through a potential V, is given by the relation: Therefore, the de Broglie wavelength of each electron is 0.1639 nm. (a) A mono-energetic electron beam with electron speed of is subject to a magnetic field of T normal to the beam velocity. Debroglie wavelength associated with an electron associated through a potential difference V is? potential), no electrons will reach the anode, i.e., Maximum kinetic energy of electron = eV, where e is charge of electron (e = 1.6 × 10. : X-rays are absorbed more in heavy elements than the lighter ones. (b) What is so special about the combination e/m? Ans.It depends upon the frequency of the incident light. Comprehend the dual nature of radiation and matter. Would a neutron beam of the same energy be equally suitable? (iii) Photoelectric current vary for different intensities but same frequency of radiations? Show that the energy of the photon is  times the kinetic energy of electron where m, c, and h have their usual meanings? (e) The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations: But while the value of  is physically significant, the value of  (and therefore, the value of the phase speed ) has no physical significance. Speed of the bullet, v= 1.0 km/s = 1000 m/s. But some features of photoelectric effect cannot be explained by classical physics & the wave theory of light. 9. Ans. Where hc/λ is energy of scattered X-rays, K, is kinetic energy of recoiling electron & hc/λ, is the energy of incoming X-rays. From the Einstein’s photoelectric equation, following points are clear: Here, vo = frequency of incident light, Φo = work function of metal, The relation between stopping potential, maximum kinetic energy and the frequency of incident light could be expressed mathematically as follows: using Einstein’s photoelectric equation. Then, J. Thomson (1856-1940) validated the above hypothesis. When light of frequency Hz is incident on the metal surface, photoemission of electrons occurs. 207, Laxmideep Building Plot No. is independent of intensity of incident light, but it depends on the frequency of incident light i.e., K. Electrons are emitted almost instantaneously consistent with particle view of light in which incident energy is concentrated in small packets (called photons) rather than over a large area (as in wave theory). However, photoelectric effect verifies the particle nature of radiations. If light of frequency Hz is incident on the metal, predict the cutoff voltage for the photoelectric emission. The phenomenon is called fluorescence. Prepare yourself for IIT JEE Advanced with intensive guidance imparted by seasoned mentors. So, this was the first inconsistency of the wave theory with the experiments. Assuming that the top 5 layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. 1)Question: Caesium metal has work function of 2.14eV. An electron and an alpha particle have the same debroglie wavelength associated with them? Ans.No, photoelectric emission is not possible at all frequencies because it is possible only if radiation energy is greater than work function  of the emitter. Hence define threshold frequency? (Photoelectric effect), Fig. 5.Ultraviolet light is incident on two photosensitive materials having work function and  ( > ). Dual Nature of Matter and Radiation. The transitions of electrons from various outer shells to the innermost ‘K’ shell produces a group of X-rays lines called as K-series. Ans. Variation of photoelectric current with the frequency of incident light: Exercise: ( Dual Nature Of Radiation And Matter ). It also is a spectrum consisting of radio waves, microwaves, infrared waves, visible light, ultraviolet radiation, X-rays, and gamma rays. We have the expression that relates mean kinetic energy of the nitrogen molecule with the root mean square speed as: Hence, the de Broglie wavelength of the nitrogen molecule is given as: Therefore, the de Broglie wavelength of the nitrogen molecule is 0.028 nm. In this experiment the pattern formed by the electrons reflected from the crystal lattice of aluminium is almost identical to that produced by X-rays. According to which, when a monochromatic beam of X-rays (wavelength λ, ) strikes the electron in a carbon target, two types of X-rays are scattered. Magnetic field experienced by the electrons, B=, Radius of the circular orbit r= 12.0 cm =. The work function of caesium metal is 2.14 eV. In 1897, he termed this negatively charged cathode ray particles as electron, and this name was used for the first time. A. MIlikan, in 1913 performed experiments to calculate the charge on an oil drop (popularly known as Milikan’s oil drop experiment), He observed that, every time the charge came to be an integral(whole number) multiple of a small charge (), which is actually the charge on an electron, MIlikan concluded that charge on a matter is quantized (discrete), The process of emission of electrons from the metal surface when a certain amount of energy is absorbed by the metal, is called electron emission, There are free electrons on the metal surface, present in the outermost (valence) shell that are loosely bound to the nucleus, These electrons are emitted when a certain minimum amount of external energy is provided to the metal surface. and wavelength of such radiation is continuous because the loss in energy is statistical. Hence, for the macroscopic objects, the mass is so large that the matter wave associated with them becomes insignificant and negligible. Electrons are emitted from surface almost instantaneously (less than 10. sec after the surface illumination), even at low intensity of incident light (classically we assume that the electrons would require some time to absorb the incident light before they acquire enough kinetic energy to escape from metal). Ans.The slope of the cut-off voltage (V) versus frequency of an incident light is given as: V is related to frequency by the equation: Therefore, the value of Planck’s constant is. Dual nature of radiation Previous JEE Mains Papers questions and solutions Download Pdf W is the threshold energy or work function depends upon threshold frequency. Explain. On further absorption of ultraviolet radiation, neutral zinc plate became negatively charged. … For 1 marker and MCQ for class 12 boards, conceptual questions from these topics as well as threshold frequency and wave function can be asked. For example, if we make blue light incident on a zinc-sulphide (ZnS) screen, then it produces phosphorescence of green colour. So, stopping potential remains unchanged, c) We also know that maximum kinetic energy, doesn’t change with intensity. (b)), we get. Here, Kmax is the maximum kinetic energy of a photoelectron. What will be the new wavelength when the accelerating potential is increase to 4V? If an electron beam of energy eV (electron volts) is incident on the target material; the electrons are suddenly stopped. 11. This λ is called de-Broglie wavelength & it is defined as : where m is the mass of matter particle & these waves are called matter waves. X-rays are electromagnetic waves. Moseley used different elements as target in the X-ray tube. (b) we consider a single drop of mass m, radius r carrying a negative charge –q in the presence of electric field acting downward. So the cracks or fracture in bones can be easily located. 9. : The X-rays of longer wavelength are called soft X-rays. At low pressures, ions have a chance of reaching their respective electrodes and constitute a current. Ans.Wavelength of the monochromatic radiation,  = 640.2 nm, Stopping potential of the neon lamp,  = 0.54 V. Let be the work function and  be the frequency of emitted light. Ans. Since  so electron being lighter will have more wavelengths. A particle of mass (m), moving with velocity (v) could behave like a wave under suitable conditions. (b) (i) Saturation current depends only on the intensity of incident radiation but is independent of the frequency of incident radiation. Hertz, in 1887 discovered the phenomena of photoelectric effect for the first time, As he was experimenting on the generation of electromagnetic waves by spark discharge, he noticed that sparks around the detector loop were intensified when ultraviolet radiation fell on the emitter plate. 24. 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