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.
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.)
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.)
Write a note on Production of low temperatures by adiabatic demagnetization.
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.
Establish that for an adiabatic process in an ideal gas T V^{\gamma-1} = \text{constant}. where the symbols have their usual meanings,
Write down the general expression for the Joule-Kelvin effect and define Joule-Kelvin coefficient, \mu. Show that for an ideal gas \mu = 0.
One gram of hydrogen gas at 27^\circ\text{C} is compressed isothermally from 100 liters to 25 liters. Calculate the energy needed.
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},
Write a note on Thermal ionization.
Derive the expression for the specific heat of solid on the Einstein model. Comment on its short-comings.
Establish the relation C_p - C_v = T \left( \frac{\partial P}{\partial T} \right)_v \left( \frac{\partial V}{\partial T} \right)_p
Show that the electric field intensity due to any distribution of charges at rest can be expressed as the gradient of a potential. What is the relation between potential and potential energy? A thin disc of radius R is uniformly charged, \sigma being the charge per unit area. Find the potential and the electric intensity at points on the axis of the disc. How do these change as one crosses the disc? Explain the changes physically.
Set up the equation for the discharge of capacitor C connected in series with a resistor R and an inductor L. If R_0 stands for 2(L/C)^{1/2}, discuss three cases: R < R_0, R = R_0 \text{ and } R > R_0 What will you observe if the discharge takes place at low temperature when the material of resistor has become superconducting?
Alpha particles of velocity v enter a uniform magnetic field in perpendicular direction. If electrons of the same velocity v enter the same magnetic field the same way compare: (i) the curvatures of their path and (ii) the tracks they would show in (say) a bubble chamber.
Two charges are placed at a distance of 1 metre. The magnitude of one charge is double that of the second charge. Find the neutral points in the two cases: (i) the charge are of the same sign (ii) the charge are of opposite sign. What happens to the neutral point if the two charges are of equal magnitude and opposite sign?
In certain region of space in vacuo, the components of the magnetic induction are (in weber per square meter) B_x = A e^{-ay} + bx B_y = A c^{-ax} + cy B_z = 0 where x, y, z, are in metres and A, a, b and c are constants. Find the relation, if any between these constants and also the current distribution that gives rise to this field. (No electric field is present). Is the current distribution consistent with the charge conservation principle?
Write down Plank's law of radiation and establish Wien's law from it.
Deduce an expression for the diffraction waves at single slit and discuss how it is related with a Fourier transform.
Write a note on Purity of spectral lines and coherence length.
