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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.
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}}.
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.
Stable light nuclei have equal number of protons and neutrons, whereas heavy nuclei have excess of neutrons. Explain why.
Explain the salient features of nuclear shell model. What are the magic numbers? Write the experimental facts in support of shell model of nuclei.
Calculate the decay rate of ^{14}\text{C} per gram of carbon in a living organism, assuming the ratio ^{14}\text{C} / ^{12}\text{C} = 1\cdot 35 \times 10^{-12}. The half-life of ^{14}\text{C} is 5730 years.
What do you understand by the reproduction factor of a fission reactor? What is the maximum value of the reproduction factor in a uranium fission reaction?
For a system consisting of one proton and one neutron (not necessarily a deuteron), write down the various possible states specifying clearly its isospin, spin and orbital quantum numbers.
Explain the origin of the nuclear magnetic moment. Deduce expression for the magnetic dipole moment with the help of the Schmidt single particle model.
Why is it not possible to detect the parity violation in weak interaction by observing only the beta decay rate? Justify your answer.
Given that the single particle energy separation between 1d_{5/2} and 1d_{3/2} in ^{17}\mathrm{O} is 5\,\mathrm{MeV}. Calculate the strength of spin-orbit interaction. It is observed that 1d_{5/2} level is lower than 1d_{3/2} level.
Explain the various methods of finding the size of the nucleus. How will you determine the nuclear radius from the observation of beta rays resulting from nuclear transition when the initial and final nuclei are mirror nuclei?
On the basis of liquid-drop model, write the semi-empirical mass formula for the total binding energy. Also explain their each term.
In the following nuclear reactions, what particles are possible for the unknown particle X?
(i) \pi^- + p \rightarrow K^0 + X
(ii) p + p \rightarrow \pi^+ + n + \Lambda^0 + X
Assuming equal masses for up (u) and down (d) quarks, find the ratio (\mu_n/\mu_p) of the magnetic moments of neutron and proton.
What are the properties of the particles made up of the following quarks? Also write the names of particles :
(i) u\bar{d}
(ii) \bar{u}d
(iii) dds
(iv) uss
By applying the conservation laws, state about the following decay equations, whether they are allowed or not allowed :
(i) \Sigma^+ \rightarrow p + \pi^0
(ii) \Sigma^0 \rightarrow \Lambda^0 + \gamma
(iii) \Lambda^0 \rightarrow n + \pi^0
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 nuclear radius of {}_8\text{O}^{16} is 3 fermi. What will be the nuclear radius of \text{U}^{235} ?