PYQ Bank

Assuming that the neutron-proton interaction has a square well form V(r)=-V_0\quad\text{for }r\leq b =0\quad\text{for }r>b, the ground state wave function of deuteron nucleus is given as \psi(r)=A\sin kr\quad\text{for }r\leq b =Ce^{-\gamma r}\quad\text{for }r>b where k=\sqrt{\frac{M}{\hbar^2}(V_0+W)} and \gamma=\sqrt{\frac{MW}{\hbar^2}}. Here M is the nucleon mass, W is the binding energy of deuteron and A and C are constants.

(i) Show that for a just bound state of deuteron V_0b^2=\frac{\pi^2\hbar^2}{4M}.

(ii) Explain why deuteron is a loosely bound extended structure.

An atomic power reactor can deliver 300\text{ MW}. If due to fission of each atom of {}_{92}\text{U}^{235}, the energy released is 200\text{ MeV}, calculate the mass of uranium fissioned per hour.

What do you mean by nuclear reactors ? With a neat diagram, describe the essential parts of a nuclear reactor and discuss about its applications.

What is the source of the Sun's energy ? Explain with proper nuclear reaction.

Which of the following elementary particle reactions/decays are allowed under various conservation laws? If allowed, write down the type of interaction and the characteristic time by which it would proceed:

(i) p + n \to \Lambda^0 + \Sigma^+

(ii) \pi^+ + n \to \Lambda^0 + K^+ \setcounter{enumi}{2}

(iii) p+n\to K^{+}+\Sigma^{+}

(iv) \pi^{0}\to\gamma+

(v) \bar{n}\to\bar{p}+e^{+}+\nu_e

The nuclear radius of {}_8\text{O}^{16} is 3 fermi. What will be the nuclear radius of \text{U}^{235} ?

Obtain an expression for the magnetic moment of a nucleus having one nucleon outside the closed core. Use this to calculate the magnetic moment of \,_{8}^{17}\mathrm{O} nucleus.

Write the semi-empirical mass formula for nuclei and on its basis draw mass parabolas for odd and even isobars. What would be the most stable isobar in each case?

The maximum energy of a positron (e^+) released in the decay of \,_{6}^{13}\mathrm{C} atom into a \,_{7}^{13}\mathrm{N} atom is 1.202\,\mathrm{MeV}. If the mass of the \,_{6}^{13}\mathrm{C} atom is 13.003354\,\mathrm{u}, calculate the mass of the \,_{7}^{13}\mathrm{N} atom.

Nuclear forces are mediated by exchange of \pi-mesons of rest mass 140\,\mathrm{MeV}. Estimate the range of nuclear forces.

Write down the semiempirical mass formula for nuclei and sketch the variation of isobaric masses with atomic number for both odd and even values of A. How many stable isobars would be there in each case ?

Predict the spin and parity for the ground state of the following nuclei on the basis of the shell model : {}_8^{15}\text{O}, {}_8^{16}\text{O}, {}_8^{17}\text{O}, {}_8^{18}\text{O}

Describe the main features of the shell model of the nucleus. Explain how it can account for the magic numbers of nuclei.

What are noncentral nuclear forces ? Discuss qualitatively how the presence of a small noncentral component in the nuclear force can account for the nonvanishing quadrupole moment of deuteron.

How much energy is required to separate {}_8^{16}\text{O} nucleus into its constituent nucleons ? What is the binding energy per nucleon for this nucleus ?

Write the semi-empirical mass formula pointing out the role of volume term, surface energy term, coulomb and symmetry energy correction terms.

How does one explain the approximate constancy of average binding energy per nucleon (\mathrm{BE}/A) of nuclei in the region 30 \leq A \leq 170 in the plot of \mathrm{BE}/A versus mass number A?

Given that the deuteron magnetic moment operator (in units of nuclear magneton) can be expressed as \vec{\mu}_d = \mu_n\vec{\sigma}_n + \mu_p\vec{\sigma}_p + \frac{1}{2}\vec{l} where \vec{l} is the relative angular momentum between neutron and proton, \vec{\sigma}_n and \vec{\sigma}_p are the Pauli spin operators and \mu_n and \mu_p are the respective magnetic moments. Find out the D-state probability of deuteron wave function. [Given: \mu_d = 0.857\mu_N, \mu_n = -1.913\mu_N and \mu_p = 2.793\mu_N; \mu_N (nuclear magneton)]

Write two properties of deuteron which support the existence of non-central tensor force.

Describe briefly how parity violation in \beta-decay was experimentally observed? What do you understand by the statement, 'neutrinos are left-handed'?