UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Derive an expression for \alpha-disintegration energy for a nucleus in a radioactive decay process.

What do you understand by nuclear forces ? Explain meson theory of exchange forces.

Why does a neutron star have a magnetic field if it is composed of neutrons?

What do you understand by the critical size of a nuclear reactor? Write down the common features of nuclear reactors used for the production of electricity.

Establish the Rutherford's scattering cross section formula for \alpha-particle by considering the standard assumptions and symbols.

What is the age of a fossil that contains 6\text{ g} of carbon {}^{14}\text{C} and has a decay rate of 27\text{ decays per minute} ? Given : Ratio \frac{{}^{14}\text{C}}{{}^{12}\text{C}} = 1\cdot 3 \times 10^{-13}, Half life (T_{1/2}) of {}^{14}\text{C} = 5730\text{ yrs}.

Which of the following decays are allowed and which are forbidden? If the decay is allowed, state which interaction is responsible. If it is forbidden, state which conservation law its occurrence would violate.

(i) n\to p+e^{-}+\bar{\nu}_e

(ii) \Lambda^{0}\to\pi^{+}+\pi^{-}

(iii) \pi^{-}\to e^{-}

(iv) \pi^{0}\to e^{-}e^{+}+\nu_e+\bar{\nu}_e

(v) \pi^{+}\to e^{+}e^{-}+\mu^{+}+\nu

Write down the Weizsäcker semi-empirical mass formula and explain each term. Explain why {}^{238}_{92}\mathrm{U} nuclide is an \alpha-emitter and not a \beta^--emitter?

Show that for a specific value (n,l), there exists a large degeneracy relative to the energy characterized by the quantum number (N). Find the shell closures and the magic numbers predicted by harmonic oscillator potential.

A reactor is developing nuclear energy at a rate of 3\cdot 2 \times 10^7\text{ watts}. How many atoms of \text{U}^{235} undergo fission per second? How many kg of \text{U}^{235} would be used up in 1000 hours of operation? Assume that an average energy of 200\text{ MeV} is released per fission. Take Avogadro number as 6 \times 10^{23} and 1\text{ MeV} = 1\cdot 6 \times 10^{-13}\text{ joule}.

A neutron and a proton can undergo radiative capture at rest: n+p \longrightarrow d+\gamma Find the energy of the photon emitted in this capture. Is the recoil of the deuteron important?

If the nuclear force is charge independent and a neutron and proton form a bound state then why is there no bound state for two neutrons? What information does this provide on the nucleon-nucleon force?

(i) The radius of a nucleus is given to be 3\cdot 46\text{ fermi}. Estimate the mass number A of the nucleus and identify the nucleus. (ii) What is Bohr magneton? Find out the ratio of nuclear magnetic moment to Bohr magneton.

What do you mean by strength of interaction among the elementary particles? Calculate the dimensionless coupling constants of gravitational and electromagnetic interactions.

(i) Show that pion decay, muon decay and pair production conserve lepton numbers L_e and L_\mu. (ii) Which of the following reactions is/are possible? Justify with reason : \bar{\nu}_e + p = n + \mu^+ \bar{\nu}_e + p \rightarrow n + e^+

Explain how the nuclear shell model predicts the existence of magic numbers. Using shell model, predict the spin parity or characteristics of ground state of {}^{15}_8\text{O}, {}^{16}_8\text{O} and {}^{17}_8\text{O}.

Write the semi-empirical mass formula. Establish the relation A \approx 2Z, where A is mass number and Z is atomic number of the light nuclei, using this semi-empirical mass formula. [Given : good fitting coefficients for Coulomb energy (a_c) = 0\cdot 71\text{ MeV}, for asymmetry energy (a_n) = 22\cdot 7\text{ MeV}]

Explain why each of the following particles cannot exist according to the quark model.

(i) A Baryon of spin 1

(ii) An anti-Baryon of electric charge +2

(i) What is Q-value and how does it help to study the kinematics of a nuclear reaction? (ii) Prove that {}^{252}\text{Cf} can undergo spontaneous fission as under : {}^{252}\text{Cf} = {}^{98}\text{Zr} + {}^{145}\text{Ce} + 9 {}^{1}\text{n} Given : \begin{aligned} M(^{252}\text{Cf}) &= 252\cdot 081621\text{ a.m.u.}\\ M(^{98}\text{Zr}) &= 97\cdot 912735\text{ a.m.u.}\\ M(^{145}\text{Ce}) &= 144\cdot 917230\text{ a.m.u.}\\ M(^{1}\text{n}) &= 1\cdot 008665\text{ a.m.u.} \end{aligned}

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