Give a brief account of Kronig-Penney model. [5]

A given spring stretches 0.1m when a force of 20N pulls on it. A 2-kg block attached to it on a frictionless surface is pulled to the right 0.2 m and released. (a) What is frequency of oscillation of the block? (b) What are the velocity and acceleration when $x=0.12\,m$, on the block's first passing this point? [5]

A proton is moving with a velocity $\vec{v} = (3 \times 10^5 \hat{i} + 7 \times 10^5 \hat{k})$ m/sec in a region where there is a magnetic field $\vec{B} = 0.4 \hat{j}$ T. Find the force experienced by the proton. [5]

The density of aluminum is $2.70 g/cm^3$ and its molecular weight is 26.98 g/mole. (a) Calculate the Fermi energy. (b) If the experimental value of $E_F$ is 12 eV, what is the electron effective mass in aluminum? [Aluminum is trivalent]. [5]

Analyze the circuit shown in the figure below. Determine the logic function performed by the circuit by making and justifying the appropriate truth table. [5]

Give spectrum of Hydrogen atom and discuss its lines. [5]

Describe the term 'space quantization'. [5]

In neutron spectroscopy a beam of mono-energetic neutrons is obtained by reflecting reactor neutrons from a beryllium crystal. If the separation between the atomic planes of the beryllium crystal is 0.732 $A^{\circ}$, what is the angle between the incident neutron beam and the atomic planes that will yield a monochromatic beam of neutrons of wavelength 0.1 $A^{\circ}$? [5]

(a) How many atomic states are there in hydrogen with n=3? (b) How are they distributed among the sub shells? Label each state with the appropriate set of quantum numbers $n, l, m_l, m_s$. (c) Show that the number of states in a shell, that is, states having the same n, is given by $2n^2$. (Hint: 1+2+3+...+n=(n(n+1)/2)). [5]