PYQ Bank

Write a short note on Gyroscope and its application.

State Bernoulli's theorem. Find out the velocity of efflux of a liquid from a reservoir in which the pressure is 3.5 \times 10^5\text{ N/m}^2 above the atmospheric pressure. The density of the liquid is 700\text{ kg/m}^3.

Write down the expression for the dependence of mass of a particle on its velocity in special relativity. What will be the speed of a particle if its mass becomes double of its rest mass ?

Write a short note on The Lorentz transformation.

The half-life of \mu-meason at rest is 2 \times 10^{-8}\text{ sec}. Determine the half life of \mu-meason while travelling with half the speed of light in vacuum.

Why do the electronic energy level in a solid form bands? Describe in terms of the band theory the difference between a conductor, an intrinsic semi-conductor and an insulator. How does the energy level change when some impurities are introduced in a semiconductor? Explain how by doping you have both n-type and p-type semiconductors starting with pure Germanium. The band gap in cases of Germanium is about 0.8\text{ eV} at Ok. Neglecting the variation of band gap with temperature, make a rough estimate of the temperature at which the resistance of a pure Germanium sample will be reduced to 1/e times its value at 300k.

Explain why Light elements like hydrogen and deuterium are effective in shielding against neutrons while heavy elements like lead are effective in case of gamma rays.

$ in keV units if E is in the range 7 meV.

Give, in short the principle of working of mass spectrograph (any type). What does it determine? What are isotopes? How many isotopes of hydrogen do you know of? Are they all stable? The minimum energy required for the disintegration of the nucleus of a stable isotope of hydrogen is 2.21\text{ MeV}. Calculate the mass of this nucleus in a.m.u.

Give the quantum numbers of the states whose energy difference accounts for the two D-lines of sodium. Find the energy difference for D_1 and D_2 lines in electron volts. (Wavelength separation = 6\text{\AA}, Mean wavelength = 5893\text{\AA})

How do characteristic X-ray lines originate? Using Bohr's atomic model deduces a relation between the frequencies of the K series X-ray lines and atomic numbers of the emitting elements. Do you expect this relation to be exact?

What are de Broglie waves? State the uncertainty principle and explain its relation with de Broglie waves by considering a free particle.

Set up Schrodinger's equation for a free particle confined in a cubical box and find the energy eigenvalues. What form will Pauli principle take for electrons in such a box? Deduce the zero point energy if the length of the box be 10^{-10}\text{ metre} and there be 10 electrons in it. (The coulomb interaction maybe disregarded.)

What is the value of the spin of the electron and the corresponding magnetic-moment? Can that be considered as arising from the classical case of rotation of a finite rigid charged body about its axis? Give reasons for your answer.

In a Compton effect experiment with incident X-ray of wavelength 0.060\text{ \AA}, one recoil electron had energy 4100\text{ eV}. Calculate the corresponding angle of scattering and the wavelength of the scattered radiation (Standard formulae may be assumed.)

A photon of energy 10\text{ eV} is scattered by an electron having an initial velocity of 1000\text{ km s}^{-1}. After the scattering the electron velocity is reduced to 200\text{ km s}^{-1}. Deduce the energy of the scattered photon.

Write down Maxwell-Boltzmann distribution for the energy of molecules of a gas at temperature T. Find the energy at which this distribution peaks. Compute in eV the mean energy of molecules of a gas at 27^\circ\text{C},

The density of steam at 100^\circ\text{C} is nearly 0.60 \times 10^{-3}\text{ kg/litre} and its latent heat is 2.31 \times 10^6\text{ J/kg}. Calculate the change in the boiling point of water if air pressure changes from 76.0\text{cm} to 70.0\text{cm} of Hg.

Write a note on Thermal ionization.

One gram of hydrogen gas at 27^\circ\text{C} is compressed isothermally from 100 liters to 25 liters. Calculate the energy needed.