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 ?
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
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
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.
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
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?
The nuclear radius of {}_8\text{O}^{16} is 3 fermi. What will be the nuclear radius of \text{U}^{235} ?
What is the source of the Sun's energy ? Explain with proper nuclear reaction.
What do you mean by nuclear reactors ? With a neat diagram, describe the essential parts of a nuclear reactor and discuss about its applications.
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.
Draw the baryon octet according to Murray Gell-Mann.
Explain briefly SU(3) flavor symmetry and SU(2) isospin symmetry in particle physics.
What is meant by quark confinement ? Why are the masses of hadrons larger than the sum of the masses of their constituent quarks ?
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}
Write the quark contents and the quantum numbers (B, J, s, I_3) of the following hadrons : \bar{\Sigma}^-, \Xi^\circ, \Pi^+, \bar{K}^\circ
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.
