The mass difference between the pair of mirror nuclei $${}_6^{11}C$$  and  $${}_5^{11}B$$ is given to be Δ MeV/c². According to the semi-empirical mass formula, the mass difference between the pair of mirror nuclei $${}_9^{17}F$$  and $${}_8^{17}O$$  will approximately be (rest mass of proton m_p = 938.27 MeV/c² and rest mass of neutron m_n = 939.57 MeV/c²)

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