What is the energy released in the process $3 \, _{2}^{4}\text{He} \to _{6}^{12}\text{C}$ (in $, \text{MeV}$)? (Mass of $_{2}^{4}\text{He} = 4.002604 \, \text{amu}$,mass of $_{6}^{12}\text{C} = 12 \, \text{amu}$)

$1 \, g$ of hydrogen is converted into $0.993 \, g$ of helium in a thermonuclear reaction. The energy released is

In the nuclear fusion reaction $_1^2H + _1^3H \to _2^4He + n$,the repulsive potential energy between the two nuclei is $7.7 \times 10^{-14} \, J$. To what temperature must the gas be heated to initiate the reaction? $[k = 1.38 \times 10^{-23} \, J/K]$

The $Q$ value of a nuclear reaction $A+b \rightarrow C+d$ is defined by $Q=\left[m_{A}+m_{b}-m_{C}-m_{d}\right] c^{2}$ where the masses refer to the respective nuclei. Determine from the given data the $Q$ value of the following reactions and state whether the reactions are exothermic or endothermic.
$(i) \;_{1}^{1} H+_{1}^{3} H \rightarrow_{1}^{2} H+_{1}^{2} H$
$(ii)\;_{6}^{12} C+_{6}^{12} C \rightarrow_{10}^{20} N e+_{2}^{4} H e$
Atomic masses are given to be:
$m(_{1}^{1}H) = 1.007825 \; u$
$m(_{1}^{2}H) = 2.014102 \; u$
$m(_{1}^{3}H) = 3.016049 \; u$
$m(_{6}^{12}C) = 12.000000 \; u$
$m(_{10}^{20}Ne) = 19.992439 \; u$
$m(_{2}^{4}He) = 4.002603 \; u$

$A$ $\gamma$-ray photon creates an electron-positron pair. If the rest mass energy of an electron is $0.51 \, MeV$ and the total kinetic energy of the electron-positron pair is $0.78 \, MeV$,then the energy of the $\gamma$-ray photon in $MeV$ is:

In an atomic bomb,the energy is released due to