PYQ Bank

State the basic conditions for oscillations in a feedback amplifier. What are the primary requirements to obtain steady oscillations at a fixed frequency?

Explain the drawbacks of Einstein's theory of specific heat and how it was overcome by Debye.

(i) Diamond and silicon have similar band structure. Why is diamond an insulator while silicon a semiconductor? (ii) An insulator has an optical absorption which occurs for all wavelengths lesser than 1400\text{ \AA}. Find the width of the forbidden energy band for the insulator.

Considering atoms hard, uniform spheres, find the number of atoms per unit cell and packing fraction for simple cubic, bcc and fcc structures.

Compare the dependence of resistance on temperature of a superconductor with that of a normal conductor. Describe briefly the formation of Cooper pairs.

The wavelength of a prominent X-ray line from a copper target is 0.1512\,\mathrm{nm}. The radiation, when diffracted with (111) plane of a crystal with fcc structure, corresponded to a Bragg angle of 20.2^\circ. If the density of the crystal is 2698\,\mathrm{kg/m^3} and atomic weight is 26.98\,\mathrm{kg/kmol}, calculate the Avogadro number.

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

(i) What is Q-value and how does it help to study the kinematics of a nuclear reaction? (ii) Prove that ^{252}\text{Cf} can undergo spontaneous fission as under : ^{252}\text{Cf} = {}^{98}\text{Zr} + {}^{145}\text{Ce} + 9 {}^{1}\text{n} Given : \begin{aligned} M(^{252}\text{Cf}) &= 252\cdot 081621\text{ a.m.u.}\\ M(^{98}\text{Zr}) &= 97\cdot 912735\text{ a.m.u.}\\ M(^{145}\text{Ce}) &= 144\cdot 917230\text{ a.m.u.}\\ M(^{1}\text{n}) &= 1\cdot 008665\text{ a.m.u.} \end{aligned}

Explain why each of the following particles cannot exist according to the quark model.

(i) A Baryon of spin 1

(ii) An anti-Baryon of electric charge +2

A reactor is developing nuclear energy at a rate of 3\cdot 2 \times 10^7\text{ watts}. How many atoms of \text{U}^{235} undergo fission per second? How many kg of \text{U}^{235} would be used up in 1000 hours of operation? Assume that an average energy of 200\text{ MeV} is released per fission. Take Avogadro number as 6 \times 10^{23} and 1\text{ MeV} = 1\cdot 6 \times 10^{-13}\text{ joule}.

Show that for a specific value (n,l), there exists a large degeneracy relative to the energy characterized by the quantum number (N). Find the shell closures and the magic numbers predicted by harmonic oscillator potential.

If the nuclear force is charge independent and a neutron and proton form a bound state then why is there no bound state for two neutrons? What information does this provide on the nucleon-nucleon force?

Explain how the nuclear shell model predicts the existence of magic numbers. Using shell model, predict the spin parity or characteristics of ground state of ^{15}_8\text{O}, ^{16}_8\text{O} and ^{17}_8\text{O}.

Which of the following decays are allowed and which are forbidden? If the decay is allowed, state which interaction is responsible. If it is forbidden, state which conservation law its occurrence would violate.

(i) n\to p+e^{-}+\bar{\nu}_e

(ii) \Lambda^{0}\to\pi^{+}+\pi^{-}

(iii) \pi^{-}\to e^{-}

(iv) \pi^{0}\to e^{-}e^{+}+\nu_e+\bar{\nu}_e

(v) \pi^{+}\to e^{+}e^{-}+\mu^{+}+\nu

(i) Show that pion decay, muon decay and pair production conserve lepton numbers L_e and L_\mu. (ii) Which of the following reactions is/are possible? Justify with reason : \bar{\nu}_e + p = n + \mu^+ \bar{\nu}_e + p \rightarrow n + e^+

A neutron and a proton can undergo radiative capture at rest: n+p \longrightarrow d+\gamma Find the energy of the photon emitted in this capture. Is the recoil of the deuteron important?

What do you mean by strength of interaction among the elementary particles? Calculate the dimensionless coupling constants of gravitational and electromagnetic interactions.

(i) The radius of a nucleus is given to be 3\cdot 46\text{ fermi}. Estimate the mass number A of the nucleus and identify the nucleus. (ii) What is Bohr magneton? Find out the ratio of nuclear magnetic moment to Bohr magneton.

Write down the Weizsäcker semi-empirical mass formula and explain each term. Explain why ^{238}_{92}\mathrm{U} nuclide is an \alpha-emitter and not a \beta^--emitter?