PYQ Bank

Which of the following reactions are possible ? (i) \quad \pi^+ + n^0 \rightarrow \Lambda^0 + K^+ (ii) \quad \pi^+ + n^0 \rightarrow K^0 + K^+ (iii) \quad \pi^+ + n \rightarrow \pi^- + p

Delhi requires 3000\text{ MWh} of electric energy per day. It is to be supplied by a reactor which converts nuclear energy into electrical energy with an efficiency of 20\text{ percent}. If reactor uses nuclear fuel of \text{U}^{235}, calculate the mass of \text{U}^{235} needed for one day operation.

(i) What is nuclear binding energy and how does it vary with mass number of the nucleus ? (ii) Calculate the binding energy per nucleon of ^{4}\text{He}. Given m (^{4}\text{He}) = 4\cdot 002602\text{ u}, m_p = 1\cdot 007825\text{ u} and m_n = 1\cdot 008665\text{ u}.

Calculate the mass of deuterium nucleus if the binding energy per nucleon is 1\text{ MeV}.

Assuming that protons and neutrons possess equal masses, calculate how many times nuclear matter is denser than water if nuclear radius is given by 1\cdot 2 \times 10^{-15} A^{1/3}\text{ m}, where A is the mass number.

Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately \hbar\omega=41A^{-1/3}\,\mathrm{MeV}.

(i) Describe the Quark model of hadrons, including the properties of quark. (ii) How does an up quark become a down quark ?

\rho^{0} and K^{0} mesons both decay mostly to \pi^{+} and \pi^{-}. Explain why the mean lifetime of \rho^{0} is shorter (\sim 10^{-23}\,\mathrm{s}) compared to the mean lifetime of K^{0} (\sim 10^{-10}\,\mathrm{s}).

What are the properties of the particles made up of the following quarks?

(i) u\bar{d}

(ii) \bar{u}d

(iii) dds

(iv) uss

A sample of uranium emitting \alpha-particles of energy 4\cdot 18\text{ MeV} is placed near the ionization chamber. Assuming that only 10 particles per second enter the chamber, calculate the current produced. Given 1 ion pair requires 35\text{ eV}.

(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})

Write down the Weizsäcker mass formula for the nuclear binding energy. Give short justification for each term of the formula.

(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}]

List in two separate columns, the quantities that are conserved and not conserved in the weak interaction of particles.

List the main reactions in the pp chain leading from hydrogen to helium during stellar nucleosynthesis. Also mention the net effect of the reactions.

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.

Explain the Mössbauer effect.

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 ?

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}}.

Write down the basic weak interaction processes in the nuclei. Also illustrate the beta decays of (i) neutron and (ii) proton.