Explain Bloch theorem. Discuss its use in Kronig-Penney model and hence in band theory. [5]

Explain the construction and working of bipolar junction transistor (BJT). [5]

A large wheel of radius 0.4 m and moment of inertia 1.2 $kgm^2$, pivoted at the center, is free to rotate without friction. A rope is wound around it and a 2-kg weight is attached to the rope. When the weight has descended 1.5 m from its starting position (a) what is downward velocity? (b) what is the rotational velocity of the wheel? [5]

An electron is placed midway between two fixed charges, $q_1 = 2.5*10^{-10} C$ and $q_2 = 5*10^{-10} C$. If the charges are 1 m apart, what is the velocity of the electron when it reaches a point 10 cm from $q_2$? [5]

Assuming that atoms in a crystal structure and arranged as close-packed spheres, what is the ratio of the volume of the atoms to the volume available for the simple cubic structure? Assume a one atom basis. [5]

The output of a digital circuit $(y)$ is given by this expression:$y = (CB + \overline{C}A)(\overline{B}A)$ where $A$, $B$ and $C$ represent inputs. Draw a circuit of the above equation using OR, AND and NOT gate and hence find its truth table. [5]

A small particle of mass $10^{-6} gm$ moves along the x axis; its speed is uncertain by $10^5 m/sec$. (a) what is the uncertainty in the x coordinate of the particle? (b) Repeat the calculation for an electron assuming that the uncertainty in its velocity is also $10^5 m/sec$. use the known values for electrons and Planck's constant. [5]

What is the probability of finding a particle in a well of width $a$ at a position $\frac{a}{4}$ from the wall if $n = 1$, if $n = 2$, if $n = 3$. Use the normalized wavefunction $\psi(x) = \left(\frac{2}{a}\right)^{1/2} \sin\left(\frac{n\pi x}{a}\right) e^{-\frac{iEt}{\hbar}}$ [5]