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}.
Establish the Rutherford's scattering cross section formula for \alpha-particle by considering the standard assumptions and symbols.
(i) K^+ \longrightarrow \Pi^+ + \Pi^+ + \Pi^- (ii) \Pi^+ + p \longrightarrow \Pi^+ + \Pi^+ + n (iii) \Pi^+ + p \longrightarrow \Delta^{++} \longrightarrow \Pi^+ + p (iv) \Sigma^\circ \longrightarrow \lambda^\circ + \gamma (v) \Sigma^+ \longrightarrow \lambda^\circ + e^+ + u_e (vi) K^- + p \longrightarrow K^+ + K^\circ + \Omega^- (vii) \Pi^\circ \longrightarrow \gamma + e^+ + e^- (viii) \Sigma^- \longrightarrow n + e^- + \bar{\nu}_e (ix) \lambda^\circ \longrightarrow p + e^- + \bar{\nu}_e (x) e^+ + e^- \longrightarrow \gamma + \gamma Name the interactions via which the above nuclear decays occur :
What do you understand by the critical size of a reactor ? Explain the main features of nuclear reactors.
What do you understand by nuclear forces ? Explain meson theory of exchange forces.
How could you establish that \nu_e and \bar{\nu}_e are two different particles ?
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
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.
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?
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?
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
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?
What are chain reactions? What do you mean by critical size of the core in which chain reaction takes place?
\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
Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately \hbar\omega=41A^{-1/3}\,\mathrm{MeV}.
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}}.
