Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
The lattice parameter and the atomic mass of a diamond crystal are 3.57\,\mathring{\mathrm{A}} and 12, respectively. Calculate the density of the crystal. Given, Avogadro's number, N = 6.023 \times 10^{26}\,(\mathrm{kg\ mol})^{-1}.
Consider atoms as hard, uniform spheres and packed closely together so that they fold touch one another. Calculate the number of atoms per cubic unit cell and fraction of volume occupied for simple cubic, body-centred and face-centred cubic structures.
In an almost pure thick aluminium sheet, there are 0.19 atomic percent of copper at the surface and 0.18 atomic percent at a depth of 1.2\,\mathrm{mm} from the surface. Calculate the flux of the copper atoms from the surface at 550^\circ\mathrm{C}, if the diffusion coefficient of copper in aluminium at this temperature is 5.25 \times 10^{-13}\,\mathrm{m^2\,s^{-1}}. Given, Al FCC with lattice parameter, a = 4.05\,\mathring{\mathrm{A}}.
What is Josephson Effect ? Give an account of applications of superconductivity.
What is an intrinsic semiconductor? Intrinsic silicon has a band gap of 1.1\,\mathrm{eV} and yet at T=300\,\mathrm{K}, the conductivity is non-zero. Explain. Comment, with the help of relevant expression, on the position of the Fermi level of an intrinsic semiconductor.
What is Meissner Effect ? Explain the validity of Meissner Effect in Type I and Type II superconductors.
Consider an amplifier with an open-loop (no feedback) gain of A and a feedback factor \beta. Derive the expression for the gain with feedback, A_f. Derive the condition for the amplifier with feedback to act as an oscillator. Comment on the change in A_f with a change in A.
Describe briefly the construction of an n-channel JFET. Define the pinch-off voltage and pinch-off current. Give the relationship between the pinch-off voltage, the saturation voltage and gate-source voltage.
A transistor operating in the CE mode draws a constant base current \text{I}_{\text{B}} of 30\ \mu\text{A}. The collector current \text{I}_{\text{C}} is found to change from 3\cdot 5\text{ mA} to 3\cdot 7\text{ mA} when the collector-emitter voltage \text{V}_{\text{CE}} changes from 7\cdot 5\text{ V} to 12\cdot 5\text{ V}. Calculate the output resistance and \beta at \text{V}_{\text{CE}} = 12\cdot 5\text{ V}. What is the value of \alpha ?
Write down the Weizsäcker mass formula for the nuclear binding energy. Give short justification for each term of the formula.
List the main reactions in the pp chain leading from hydrogen to helium during stellar nucleosynthesis. Also mention the net effect of the reactions.
Show that pion decay, muon decay and pair production conserve the Lepton numbers \text{L}_{\text{e}} and \text{L}_{\mu}.
Explain the classification of elementary particles and discuss their interactions.
A nuclear reactor using ^{235}_{92}\text{U} is to operate at a power level of 250 megawatt. If the energy released per fission of ^{235}_{92}\text{U} is 200\text{ MeV}, calculate the rate of consumption per year.
Natural uranium found in the earth's crust contains the isotopes ^{235}_{92}\mathrm{U} and ^{238}_{92}\mathrm{U} in the atomic ratio 7\cdot3\times10^{-3} to 1. Assuming that at the time of formation these two isotopes were produced equally, estimate the time since formation. Given that the mean lives of both the isotopes are 1.03\times10^{9} years and 6.49\times10^{9} years, respectively.
Write down the basic weak interaction processes in the nuclei. Also illustrate the beta decays of (i) neutron and (ii) proton.
Discuss in brief any two basic nuclear properties. Find the nuclear radius of ^{12}_{6}\text{C} nucleus. Compare the atomic radius of carbon C-12 to the nuclear radius assuming the atomic radius to be 0\cdot 529 \times 10^{-10}\text{ m}. (R_0 = 1\cdot 2\text{ fm}) What inference will you get from the comparison with regards to nuclear size of carbon ?
Explain the Mössbauer effect.
(i) Plot mass number A versus binding energy per nucleon. How does this curve help to explain the nuclear fission and fusion ? (ii) In their old age, heavy stars obtain part of their energy by the following nuclear reaction {^{4}_{2}\text{He}} + {^{12}_{6}\text{C}} = {^{16}_{8}\text{O}}. How much energy does each such event give off ? [\text{Given : } {^{4}_{2}\text{He}} = 4\cdot 002603\text{ u}, {^{12}_{6}\text{C}} = 12\cdot 000000\text{ u}, {^{16}_{8}\text{O}} = 15\cdot 999\text{ u}]
(i) Write semi-empirical mass formula for the nuclei. Discuss in brief the physical significance of each term. (ii) The meson theory of nuclear forces assumes the virtual exchange of pions. If a nucleon emits a virtual pion of rest mass 270\text{ m}_{\text{e}}, calculate the range of the nuclear force. (\text{m}_{\text{e}} is the mass of electron = 9\cdot 11 \times 10^{-31}\text{ kg})