State Kepler's laws of planetary motion. Assume the law of gravitation to be of the form F = mMG/r^n where n is some number. Find the value n which will be consistent with Kepler's third law. For this you may assume planetary orbits to be circular.
A satellite moves round the earth at a distance of 3.884 \times 10^5\text{ km} from its centre. Find its period of revolution in days. Proceed dto deduce the distance for a geostationary satellite.
Define differential, scattering cross-section. Write down the dependence of Rutherford scattering cross-section \sigma(\theta), on the scattering angle \theta and sketch this dependence graphically. In the present case, the total scattering cross-section, \sigma = \int \sigma(\theta) d\Omega turns out to be infinite. Comment on this result.
A neutron of energy 1.00\text{ MeV} collides with a stationary helium nucleus and is scattered. Deduce the momentum of the neutron and the helium nucleus in their centre of mass system.
State the difference in the electronic energy states in an isolated atom and in a solid. Hence explain difference between a conductor, an insulator and an intrinsic semiconductor. What is the role of impurities in so-called extrinsic semiconductors?
Considering the electrons in the atom, what is the difference between a diamagnetic and a paramagnetic substance? State how magnetic the susceptibility varies with temperature for dia, para, ferro- and anti-ferro-magnetic materials. (No theoretical discussion required.)
What is a Zener diode? Explain what function it performs in the circuit given below as the load resistance R_L is varied. What is the purpose of introducing resistor R_2 in the circuit? (V_s and R_s represent source voltage and resistance, respectively).
Given a rough sketch showing the variation of binding energy per nucleon with mass number of nuclei and hence explain how an enormous amount of energy is emitted in uranium fission. How it is that two blocks containing uranium of mass number 235 may remain quiet when separated but may explode when brought together into a single block? Explain the function of a moderator in a nuclear reactor.
Explain why a cyclotron is used for accelerating particles like Protons and deuterons but is not used for accelerating electrons. Mention the advantages and disadvantages of a linear accelerator compared to cyclic accelerators like the cyclotron.
What did the Stern-Gerlach experiment establish? Explain your answer. Would the experiment succeed if it were performed with a beam of free electrons?
Write an explanatory outline of thermal ionization of atoms and the spectra of stars, specifying what information we get from the latter.
What is meant by L-S coupling? Deduce the spectral terms which can arise from 3p4p electron configuration. Would all these terms exist in 3\mathrm{p}^2 configuration? Write expressions for the square of angular momentum for L=2 and also for the component of angular momentum for \mathrm{m}_j=2 as given by quantum mechanics.
Photoelectron are liberated by ultraviolet light of wavelength 3000\text{ \AA} from a metallic surface for which the photoelectric threshold is at 4000\text{ \AA}. Calculate the De Broglie wavelength of electrons emitted with maximum kinetic energy.
In a hydrogen atom the electron is replaced by a muon whose mass is 200 times that of the electron and charge is the same as that of the electron. Calculate the Ionization potential on the basis of Bohr's model.
Write down Schrodinger's equation in one-dimension and explain the significance of the eigenvalues and eigenfunction of this equation. Solve the Schrodinger's equation if the potential function V is given as V(x) = V_e(\text{a constant}) for |x| < a/2 = 0 for |x| > a/2 State the boundary conditions you use along with their justification (In the solution consider particles incident from one side only.) If he total energy F < V_0 show that there is an important difference with classical mechanics. Explain with the help of the uncertainty principle that E < V_0 does not mean that the kinetic energy is negative.
In a Compton scattering the angle of scattering was 30^\circ while the angle of recoil was 60^\circ. Calculate the energy of the incident photon taking the formulae you use as given.
Obtain the Clausius-Clapeyron equation. \frac{dp}{dt} = \frac{L}{T(v_2 - v_1)} where the symbols have their usual meanings
How much faster does a cup of coffee cool when it is at 100^\circ\text{ C} than when it is at 30^\circ\text{ C}, if room temperature is 20^\circ\text{ C}?
Write a short note on Thermodynamic potentials.
Explain, using the kinetic modal, why peaks in the curves showing Maxwell distribution of molecular speeds move towards higher speed at higher temperature.
