Two spin-1/2 fermions having spins $$\overrightarrow {{S_1}} $$ and $$\overrightarrow {{S_2}} $$ interact via a potential $$V\left( r \right) = \overrightarrow {{S_1}} .\overrightarrow {{S_2}} \,{V_0}\left( r \right).$$    The contributions of this potential in the singlet and triplet states, respectively are

Which one of the following disintegration series of the heavy elements will give ²⁰⁹Bi as a stable nucleus?

A. Thorium series

B. Neptunium series

C. Uranium series

D. Actinium series

The lifetime of an atomic state is 1ns. The natural line width of the spectral line in the emission spectrum of this state is of the order of

A. 10^-10 eV

B. 10^-9 eV

C. 10^-6 eV

D. 10^-4 eV

The quark content of $$\sum {^ + } ,\,{K^ - },\,{\pi ^ - }$$   and p is indicated: $$\left| {\sum {^ + } } \right\rangle = \left| {uus} \right\rangle ;\,\left| {{K^ + }} \right\rangle = \left| {s\overline u } \right\rangle ;\,\left| \pi \right\rangle = \left| d \right\rangle ;\,\left| p \right\rangle = \left| {uud} \right\rangle $$
In the process, $${\pi ^ - } + p \to {K^ - } + \sum {^ + } ,$$     considering strong interactions only, which of the following statements is true?

A. The process is allowed because ΔS = 0

B. The process is allowed because $$\Delta {I_3} = 0$$

C. The process is not allowed because ΔS ≠ 1 and $$\Delta {I_3} \ne 0$$

D. The process is not allowed because the Baryon number is violated

The four possible configurations of neutrons in the ground state of $${}_4^9Be$$  nucleus according to the shell model, and the associated nuclear spin are listed below. Choose the correct one

A. $${\left( {{}^1{s_{1/2}}} \right)^2}{\left( {{}^1{p_{3/2}}} \right)^3};\,J = \frac{3}{2}$$

B. $${\left( {{}^1{s_{1/2}}} \right)^2}{\left( {{}^1{p_{1/2}}} \right)^2}{\left( {{}^1{p_{3/2}}} \right)^1};\,J = \frac{3}{2}$$

C. $${\left( {{}^1{s_{1/2}}} \right)^1}{\left( {{}^1{p_{3/2}}} \right)^4};\,J = \frac{1}{2}$$

D. $${\left( {{}^1{s_{1/2}}} \right)^2}{\left( {{}^1{p_{3/2}}} \right)^2}{\left( {{}^1{p_{1/2}}} \right)^1};\,J = \frac{1}{2}$$