UPSC Physics Optional PYQs (CSE & IFoS)PYQs

The following common-emitter amplifier is required to have a signal voltage gain V_{\text{out}} / V_S of at least 100. The transistor has \beta = 63, early voltage V_A = 100\text{ V} and I_{SE} = 1.5 \times 10^{-14}\text{ A} :

Assuming that the operating collector voltage is supposed to be + 6\text{ V}, perform related calculations to check whether the circuit satisfies the operating point and voltage gain criteria. The reactance of the capacitors can be neglected at all frequencies.

What are Brillouin zones ? How are they related to the energy levels of an electron in a metal ? Draw the Brillouin zone for a rectangular lattice of sides \pi and 2\pi. Also compute the energy at the corner and midpoints of the adjacent sides of the first Brillouin zone.

What is a microprocessor ? Explain the internal architecture of an 8085 \mu\text{P}.

Explain the working and applications of a FET.

(i) Simplify the logical expression f = ABC + B \overline{C} D + \overline{A} BC by using Karnaugh map and realise f using NAND gates only. 10 (ii) The transistor in the following circuit has \beta = 100 and V_A = 90\text{ V}. What value of R_B will give 0 volt d.c. output 10

Illustrate the Geiger-Nuttall law in a plot between the decay constant and energy of various nuclides for any radioactive series.

(i) Exlain the quark structure of hadrons. Identify the field of quark of electro-weak and electro-strong interactions. Also verify the conservation of strangeness in the following reactions : 10 \pi^- + p \rightarrow \Lambda^\circ + K^\circ K^+ \rightarrow \pi^+ + \pi^+ + \pi^- (ii) Drawing necessary diagrams, explain diamond structure and CsCl structures. 10

(i) Discuss in detail the classification of elementary particles. 10 (ii) On the basis of band theory, explain the classification of solids by considering their electrical properties. 10

In the following reactions indicate with an explanation, whether they proceed by strong, electromagnetic or weak interaction or they are forbidden : \pi^+ \rightarrow \mu^+ + u_\mu p \rightarrow n + e^+ + u_e p + \pi^- \rightarrow K^+ + \Sigma^-

What is the role of neutrino in the weak interaction of radioactive nuclides ? Explain the experimental detection of neutrino.

Name the various classifications of the gamma rays based on electric, magnetic and order. How does parity affect these radiations ?

Describe briefly the different types of physical processes with which gamma rays are absorbed by matter as they are emitted.

Based on physical calculations, explain why deuteron is stable.

What are the gyromagnetic factors of the three cases, viz., a spinning electron, an orbiting electron and a free proton ?

Determine the order of magnitude of the energy involved in the spin-orbit interaction of 2p state of an atom with an electron. Given the magnetic field due to the state is 0.28 T.

Explain and discuss the basic principle of nuclear magnetic resonance (NMR).

State and discuss the Franck-Condon principle giving special reference to its applications.

Examine whether the molecule {}^{11}\text{B}^{16}\text{O} can show – (i) a pure rotation spectrum ; (ii) a vibration-rotation spectrum. Give reasons.

(i) Using Pauli matrices \sigma_x, \sigma_y and \sigma_z, show that \left(\vec{\sigma} \cdot \vec{r}\right) \left(\vec{\sigma} \cdot \vec{p}\right) = \vec{r} \cdot \vec{p} + i \vec{\sigma} \cdot \vec{L} \quad 10 (ii) For the radiation of wavelength 6000~\text{\AA}, determine the wavelength separation between its two component lines which are observed in the normal Zeeman effect. The magnetic field used is \frac{\pi}{4}~\text{weber}/\text{m}^2 and the specific charge of the electron = 1.76 \times 10^{11}~\text{C}~\text{kg}^{-1}. 10

(i) Calculate the de Broglie wavelength of a thermal neutron at 27~^\circ\text{C} temperature. 10 (ii) Considering one-dimensional case for free particle, show that the plane wave function is the eigenfunction of a linear momentum operator and kinetic energy operator. 10