Unit 1 Question Bank Suggested questions 1. 2. 3. 4. 5. 6. State and explain the laws relating to radiation and temperature of a radiating body. State and explain Stefan-Boltzmann law. State and explain Wein’s displacement law. What is a blackbody? Give Planck’s hypothesis. Discuss Planck’s radiation law. “Photoelectric effect is a frequency dependent phenomenon and not intensity dependent one”. Explain. 7. What are the failures of classical electromagnetic theory in explaining the photoelectric effect? 8. The photon model succeeds whereas the wave model fails in explaining the photoelectric effect. Explain. 9. In a photoelectric effect, explain how a change in intensity and frequency affects the number of photoelectrons and the kinetic energies of these electrons, on the basis of Einstein’s theory. 10. Explain Compton effect and derive expression for Compton shift with the help of a suitable diagram. 11. What is de Broglie hypothesis? 12. Show how one can arrive at Bohr’s quantization condition on the basis of de Broglie’s hypothesis of matter waves. 13. Describe an experiment that verifies the de Broglie hypothesis. 14. State and explain Heisenberg’s uncertainty principle. 15. Using Heisenberg’s uncertainty principle prove that electrons can’t exist inside a nucleus. 16. Find the radius of the first Bohr orbit using the Heisenberg’s uncertainty principle. Numerical Problems 1. Light of wavelength 2000 Å falls on an aluminium surface with work function 4.2 eV. Calculate (i) threshold wavelength and (ii) stopping potential. [Ans: (i) 2952 Å (ii) 2eV] 2. Work function of Na is 2.3 eV. Obtain the maximum wavelength which will cause emission of photoelectrons from the material. What will be the maximum kinetic energy of the photoelectrons emitted by the surface exposed to the radiation of 2000 Å. [Ans: (i) 5391 Å (ii) 3.9 eV]. 3. The work function for cadmium is 4.08 eV. What must be the wavelength of radiation incident on cadmium so that the maximum velocity of photoelectrons will be 7.2 x 105 m/s. [Ans: 2234 Å]. 4. X-rays of 0.5 Å are scattered by free electrons in a block of carbon through 90°. Find the velocity of recoil electrons. [Ans: 2 x 107 m/s]. 5. X-ray photon of wavelength 0.3 Å is scattered through an angle 45° by a loosely bound electron. Find the wavelength of scattered photon. [Ans: 0.307 Å]. 1 6. X-rays with initial wavelength 0.5 x 10-10m undergo Compton scattering. For what scattering angle is the wavelength of the scattered X-rays greater than that of the incident X-rays by one percent? [Ans: 37.4°]. 7. A black body radiator at 0°C radiates energy of 3.2 x 102 J.m-2.s-1. Deduce the value of Stefan’s constant. [Ans: 5.7 x 10-8 J.m-2.s-1.K-4]. 8. Using Wein’s displacement law, estimate the temperature of sun. Given: λm = 4900 Å and Wein’s constant = 0.292 cm. K. [Ans: 5963 K] 9. An electron beam is accelerated from rest through a potential difference of 200 V. (i) Calculate the associated wavelength. (ii) This beam is passed through a diffraction grating of spacing 3 Å. At what angle of deviation from the incident direction will be the first maximum observed? [Ans: (i) 0.86 Å (ii) 8.31°]. 10. An enclosure filled with He is heated to 400 K. A beam of He atom emerges out of the enclosure. Calculate the de Broglie wavelength corresponding to He atoms. Mass of He atom is 6.7 x 10-27 kg. [Ans: 0.769 Å]. 11. What is the wavelength of the wave associated with an electron having kinetic energy of 100 eV? [Ans: 1.22 Å] 12. A spectral line of wavelength 6000 Å has a width of 5 x 10-5 Å. Determine the minimum time spent by the atomic system in the associated energy state. [Ans: 3.82 x 10-8 s] 13. An electron is confined to a box of length 10-8 cm. Calculate the minimum uncertainty in its velocity. [Ans: 1.16 x 106 m/s]. 14. If the kinetic energy of an electron known to be about 1 eV must be measured to within 0.0001 eV, what accuracy can its position be measured simultaneously. [Ans: 1.95 μm]. 15. An electron and a 150 g base-ball are travelling at a velocity of 220 m/s, measured to an accuracy of 0.005 %. Calculate and compare uncertainty in position of each. [0.4 mm; 2.5 x 10-3 m]. 2