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}}.
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.
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.
Verify the following Boolean identities : (i) A + \bar{A} B = A + B (ii) \overline{\bar{A} + B} + \overline{\bar{A} + \bar{B}} = A
Describe the basic segments of a microprocessor and briefly mention their functions. Mention the name of widely used 8-bit microprocessors.
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.
What is Josephson Effect ? Give an account of applications of superconductivity.
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 ?
(i) Plot proton number (Z) versus neutron number (N). What is the inference from the plot with regards to light and heavy nuclides ? (ii) Which nucleus would you expect to be more stable, {}^{7}_{3}\text{Li} or {}^{8}_{3}\text{Li} ? Justify your answer.
Show that pion decay, muon decay and pair production conserve the Lepton numbers \text{L}_{\text{e}} and \text{L}_{\mu}.
(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})
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 ?
(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}]
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.
Explain the classification of elementary particles and discuss their interactions.
List in two separate columns, the quantities that are conserved and not conserved in the weak interaction of particles.
Write down the basic weak interaction processes in the nuclei. Also illustrate the beta decays of (i) neutron and (ii) proton.
List the main reactions in the pp chain leading from hydrogen to helium during stellar nucleosynthesis. Also mention the net effect of the reactions.
Calculate in terms of the nuclear magneton, \mu_{\mathrm{N}}, the magnetic dipole moment of {}^{3}S_{1} state of deuteron. Given, \mu_{\mathrm{p}}=2\cdot792847\mu_{\mathrm{N}} and \mu_{\mathrm{n}}=-1.913042\mu_{\mathrm{N}}.
