Modern Physics — DU B.Sc. (Hons) Physics Previous Year Question Papers

4. Answer any four of the remaining five questions. (a)Calculate the mass defect of 𝐻𝐻𝐻𝐻2 4 . Given: Mass of proton = 1.00728 u, Mass of neutron = 1.00866 u, mass of helium nucleus = 4.00150 u. (b) An X-ray photon of wavelength 0.5 nm is scattered through an angle of 60𝑜𝑜. Calculate the change in wavelength. (c) Define group velocity and phase velocity. (d) What is the significance of Planck’s constant in the uncertainty principle? (e) What are the essential components of a laser system? (f) For a crystal with spacing 𝑑𝑑= 0.3 𝑛𝑛𝑛𝑛, X-rays of wavelength 0.1 𝑛𝑛𝑛𝑛 are used. Find the angle for second-order diffraction. (g) Explain the lower binding energy of lighter nuclei. 1-(a)Explain the experimental setup and working of the Davisson–Germer experiment. How did it demonstrate the wave nature of electrons? (b)A wave is described by the dispersion relation: (i) Phase velocity (ii) Group velocity 2(a) Explain the gamma-ray microscope thought experiment and show how it leads to the uncertainty in position and momentum. (b) An electron is confined within a region of width 1.0 × 10−8𝑛𝑛. Find the minimum uncertainty in its momentum and velocity. 3(a) Compare the behavior of photons and electrons in the two-slit experiment. What conclusions can be drawn about the nature of matter and radiation? (b) In a double-slit experiment, slit separation 𝑑𝑑= 4λ and slit width 𝑎𝑎 = λ . Find the first missing order. (8) 4(a) Explain the process of lasing action in a laser system. How does the population inversion created within the gain medium lead to the emission of coherent light? (10) b) For a system, 𝐴𝐴21 = 2.0 × 10−7s−1and energy density of radiation 𝑢𝑢(𝜈𝜈) = 10−5 J/m−3 , find the ratio of stimulated to spontaneous emission rates. 5 (a) Write down the assumptions and draw backs of Liquid drop model. Derive the Semi empirical binding-energy formula. (b) Calculate the binding energy of (Z=13, A=27). Use (in MeV): 𝑎𝑎𝑣𝑣 6(a) Discuss the conservation laws involved in beta decay and explain how the neutrino ensures their validity. (10) (b) Explain the N–Z graph and discuss its significance in understanding nuclear stability.