1.
Find the energy, momentum and wavelength of a photon emitted by a hydrogen atom making a direct transition from an excited state with n 10 to the ground state. Also find the recoil speed of the hydrogen atom in this process.

An electron is confined to move between two rigid walls separated by 10-9 m. Compute the de Broglie wavelengths representing the first three allowed energy states of the electron and the corresponding energies.

A typical atomic radius is about 5 x 10^-15 m and the energy of l3-particle emitted from a nucleus is at most of the order of 1 MeV. Prove on the basis of uncertainty principle that the electrons are not present in nuclei.

In the Stern-Gerlach experiment using Ag atoms, the oven temperature is 1000 l 25cm and dBz/dz 10+3 Tesla/m. Calculate the separation of the two components.

Using uncertainty principle, calculate the size and energy of the ground state of hydrogen atom.


2.
Describe Stern-Gerlach experiment. Discuss how it has explained space quantization and electron spin. Find the value of angle between the spin angular momentum S and its z-component of an electron moving along the external magnetic field B.

The series limit wavelength of Balmer series in hydrogen spectrum is experimentally found to be 3646 A. Find the wavelength of the first line of this series.

Compute the allowed spectral terms for two non-equivalent p-electrons on the basis of Pauli's exclusion principle.

3.
What is Raman effect? Describe briefly the chief characteristics of pure rotational spectra. The small rotational Raman displacement for HCl molecule is 41.6 Find the internuclear distance between the atoms forming the molecule.

Explain in detail L-S coupling and j-j coupling schemes.

What is Lamb shift What is its significance in determining the fine structure of Ha Blalmer line in hydrogen atom?

4.
Solve the Schrodinger equation for a step potential and calculate the transmission and reflection coefficient for the case when the kinetic energy of the particle Eo is greater than the potential energy V

Write down the matrix representation of the three Pauli matrices sigma x ,sigma y ,sigma Z. Prove that these matrices satisfy the following identities:


src='./qimages/8074-4b.jpg'>



if A and B commute with Pauli matrices.

Calculate the density of states for an electron moving freely inside a metal with the help of quantum mechanical Schrodinger's equation for free particle in a box.

5.
Explain why the deuteron has no excited state.

Why are NAND and NOR gates called universal gates? Give the logic diagram, Boolean equation and the truth table of a NAND gate.

What are elementary particles and how are they classified? Describe in brief the different types of interactions that can occur between the elementary particles.

The primitive translation vectors of a two-dimensional lattice are

a b 2j . Determine the primitive translation vectors of its reciprocal lattice.

With the help of a schematic diagram, show how entropy and specific heat vary with temperature for a superconductor.

6.
State the basic assumption of single particle shell model. How do the centrifugal and spin-orbit terms remove the degeneracy of a three-dimensional spherical harmonic oscillator?

Show that in the nuclear shell model, the level spacing between major
oscillator shells is approximately hw =41 MeV.

Predict the spin and parity of ground states of the following nuclei on the basis of shell model

src='./qimages/8074-6c.jpg'>

7.
Explain the various leptonic family members. What is leptonic number conservation Based on this conservation law, state whether the following reactions are possible or not:


src='./qimages/8074-7a.jpg'>



Write down the quark structure of the following hadrons
src='./qimages/8074-7b1.jpg'>

Write down the following decays in terms of quarks

src='./qimages/8074-7b2.jpg'>

Explain unification of electromagnetic and weak interactions. What is Zo-boson What is its relevance in electroweak unification?

8.
What is the difference between direct .and indirect band gap semiconductors? Which one is suitable for use in solar cells?

Obtain Laue's equations for X-ray diffraction by crystals. Show that
these are consistent with the Bragg's law.

Write down the salient features of the Einstein's theory of lattice heat
capacity. Further write down the expression for specific heat in Einstein's theory and explain its high and low temperature limits.