A power supply using a full-wave rectifier is to provide 100\text{ mA} at 20\text{ V} with no more than 1\% ripple. Calculate the minimum value of smoothing capacitor used. Consider the diode resistance and the resistance of the secondary of the transformer as negligible. Also take ripple frequency as 50\text{ cycles per second}.
For a simple cubic, a face centered cubic and a body centered cubic crystal, determine the atomic packing factor. How many atoms per \text{mm}^2 surface area are there in (100) plane for leads which has f.c.c. structure. The radius of the atoms is 0\cdot 174\text{ nm}.
(i) What is De Morgan's law ? (ii) Simplify the Boolean expression A + AB + ABC + ABCD
(i) Explain how the helicity of neutrino can be measured. (ii) What are 'strange particles' and what is 'strangeness number' ?
What is Q value of a nuclear reaction ? Obtain an expression for the Q-value in terms of mass and energy of the particles.
On the basis of binding energy curve explain why energy is released both in Fission and Fusion.
Discuss the four basic types of fundamental interactions in nature and compare them.
Calculate the two longest wavelengths of the Balmer series of triply ionized beryllium (z = 4).
Derive the rotational-vibrational energy levels of a diatomic molecule. Give the analysis of the spectral lines.
Discuss the pure rotational Raman spectra of symmetric top molecules. What are R and S branches ?
(i) Explain 'term symbol' for a particular atomic state. (ii) Show that the spectral lines of alkali metals are doublets.
Starting from Schrödinger equation obtain an expression for the probability current density. Hence give an interpretation to the wave function.
A lead ball of mass 0\cdot 1\text{ g} is thrown with a velocity of 10^3\text{ cm/sec} through a hole 1\text{ cm} in radius. Calculate the uncertainty in the angle of emergence.
Solve the Schrödinger equation for a gas of non interacting electrons enclosed in a cube of volume L^3. What do you mean by density of states ? Calculate the density of states and Fermi energy for the above system.
What do you understand by expectation value ? Prove that \frac{d}{dt}\langle x\rangle = \frac{1}{m}\langle p_x\rangle
(i) Show that the orientation of the spin angular momentum vector of an electron with respect to the z-axis is less than one radian for spin up electron. (ii) When the orbital angular momentum vector \vec{L} has the magnitude \sqrt{6}\hbar, calculate the L_z components. What angles does the \vec{L} vector make with the z-axis ?
Solve the Schrödinger equation to obtain the energy levels and eigenfunctions of a particle in a one dimensional infinitely deep potential well given by \begin{aligned} V(x) &= 0 \text{ for } 0 < x < a \\ &= \infty \text{ for } x < 0 \text{ and for } x > a \end{aligned} Show that they form an orthonormal set of functions. What do you understand by completeness condition ? Show that they form a complete set of functions.
Find the efficiency of a Carnot's engine working between 127^\circ\text{C} and 27^\circ\text{C}.
A motor car tyre has a pressure of 2\text{ atmospheres} at the room temperature of 27^\circ\text{C}. If the tyre suddenly bursts, find the resulting temperature.
Derive the gas equation when it undergoes adiabatic process.
