PHOTOELECTRIC EFFECT NUMERICALS - CHAPTER 14 - DUAL NATURE OF RADIATION AND MATTER SOLUTIONS
7. What will be the energy of each photon in monochromatic light of frequency 5x 10^14 Hz?
8. Observations from an experiment on photoelectric effect for the stopping potential by varying the incident frequency were plotted. The slope of the linear curve was found to be approximately 4.1x l0^-15 V s. Given that
charge of each electron is 1.6*10^-19 C - find the Planck's constant h.
9. The threshold wavelength of tungsten is 2.76 x 10^-5 cm. (a) Explain why no photoelectrons are emitted when the wavelength is more than 2.76 x 10^-5 cm. (b) What will be the maximum kinetic energy of electrons ejected in each of the following cases (i) if ultraviolet radiation of wavelength X = 1.80 x 10^-5 cm and (ii) radiation of frequency 4x 10^15 Hz is made incident on the tungsten surface. [Ans: 2.40 eV, 12.07 eV]
10. Photocurrent recorded in the micro ammeter in an experimental set-up of photoelectric effect vanishes when the retarding potential is more than 0.8 V if the wavelength of incident radiation is 4950 A. If the source of incident radiation is changed, the stopping potential turns out to be 1.2 V. Find the work function of the cathode material and the wavelength of the second source. [Ans: 1.71 eV, 4270 A]
II. Radiation of wavelength 4500 A is incident on a metal having work function 2.0 eV. Due to the presence of a magnetic field B, the most energetic photoelectrons emitted in a direction perpendicular to the field move along a circular path of radius 20 cm. What is the value of the magnetic field B? [Ans. : 1.47 x 104 T]
12. Given the following data for incident wavelength and the stopping potential obtained from an experiment on photoelectric effect, estimate the value of Planck's constant and the work function of the cathode material. What is the threshold frequency and corresponding wavelength? What is the most likely metal used for emitter?
13. Calculate the wavelength associated with an electron, its momentum and speed (a) when it is accelerated through a potential of 54 V, [Ans: 0.167 nm, 39.70 x10.23 kg m s•', 4.36 x106 m s•l] (b) when it is moving with kinetic energy of 150 eV. [Ans: 0.100 nm, 66.13x10.23 kg m s•1, 7.26 x106 m ]
14. The de Broglie wavelengths associated with an electron and a proton are same. What will be the ratio of(i) their momenta (ii) their kinetic energies? [Am: 1,1836]
15. Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an a-particle, what are the possibilities for the other particle? [Ans: proton or neutron]
16. What is the speed of a proton having de Broglie wavelength of 0.08 A? [Ans: 49.57 x 10^3 m
17. In nuclear reactors, neutrons travel with energies of 5 x 10'21 J. Find their speed and wavelength. [Ans: 2.45 x 103 m s.', 1.62 A]
18. Find the ratio of the de Broglie wavelengths of an electron and a proton when both are moving with the (a) same speed, (b) same energy and (c) same momentum? State which of the two will have the longer wavelength in each case? [Ans: (a) 1836, (b) electron; 42.85, electron; (c) 1, equal]
