Give an example of nuclear fusion and explain how energy is released in the process. In nature fusion reactions are often brought about by height temperatures. Explain the role of high temperature and the relevance of quantum effect in this.
Write a brief scientific note on Elementary particles and their classification.
Radium has a half-life of 1600 years and the daughter nucleus Radon also decays with a half-life of 3.82 days. In an enclosure containing radium and radon gas, the amount of radon appears to be constant for observations extending over a week. Explain this and calculate the ratio of the numbers of radium nuclei. Will the amount of radon remain the same even after 400 years?
Write a brief scientific note on Linear particle accelerators.
Two isotopes of oxygen have nuclear masses 15.990523 a.m.u. and 17.994768 a.m.u. Calculate the binding energy per nucleon in the two cases in MeV. What do you expect about the relative abundances of the two isotopes?
What are the transitions leading to the emission of the D lines of Sodium? Deduce the expression for the Lande splitting factor. g and calculate its values for the states involved in the emission of D lines. Hence find the change of energies of these levels when a sodium source is placed in a magnetic field which is not too high.
Discuss how stars are classified on the basis of their spectra. Briefly mention what different informations about stars can be obtained from the study of their spectra.
What are anti-Stokes lines? Do they occur in both Raman and Compton scatterings? Explain how they arise and how temperature affects their intensities.
State de Brogue hpotliesis and use it to deduce the energy levels of a particle in a one-dimensional box. Calculate the mean energy per electron at 0\text{ K} if electrons arc enclosed in a long-chain molecule of length 50\text{ \AA}.
State the important points in Bohr's theory of the hydrogen atom winch depart from classical ideas. Flow is the idea of Bohr orbits changed in Schrodinger's wave mechanics?
Set up Schrodinger's equation for a one dimensional harmonic oscillator. Assuming that the solution is of the from \psi = A e^{-\alpha x^2} f(x) where \alpha is a constant and f(x) is a polynomial in x, find the energy eigen values and the ground state eigenfunction. Comment on the relation between the ground slate energy and Heisenberg's uncertainty principle.
Calculate the work done in compressing adiabatically 10^{-3}\text{ kg} of air initially at STP to one-half its original volume. (Give density of air at \text{STP}=1.293\text{ kg/m}^3 and \gamma = 1.4.
A system is composed of two-level atoms, the excited state 1, being 0.10\text{ eV} above the ground state 0. Find the fraction of all atoms which will be in state 1 if the system is in thermal equilibrium at temperature 300\text{ K}.
Write down the Maxwell-Boltzmann law for the distribution of speeds c of molecules in a gas. Show the distribution graphically for the temperatures T and 2T; also write down the expression for average value of c^3.
Calculate the mean free path of molecules of \text{H}_2 gas at 20^\circ\text{ C} at atmospheric pressure. Assume the molecular diameter to be 2.00 \times 10^{-10}\text{ m}.
Write a note on Enthalpy as a thermodynamic potential.
Thermal energy of a solid is given by the relation E = \int_0^{ u_m} \frac{h\nu g(\nu)d\nu}{e^{h\nu/k_B T} - 1} where u_m = k_B \theta_D/h, \theta_D being the Debye temperature. Given g(\nu) = 6N h^2 \nu(k_B \theta_D)^2, deduce the expression for E for T \ll \theta_D and discuss the temperature variation of specific heat for T \ll \theta_D. \left( \int_0^\infty \frac{x^3 dx}{e^x - 1} = 2.404 \right)
Write a note on Dilution refrigeration.
A charged particle moving horizontally towards the east with a velocity of 10^{5}\text{ m/s} enters into a region where there is a horizontal electric field E intensity 100\text{ volt/cm} directed towards the north as also a magnetic field B. The particle continues to move in the same direction as before. What can you san about the field B? Is it completely determined? What will be the path, of particle if the magnetic Field be switched off?
Write a brief scientific note on Ferrimagnetism and ferrites.
