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? $[k = 1.38 \times 10^{-23} \, J/K]$

What was the fissionable material used in the bomb dropped at Nagasaki (Japan) in the year $1945$?

The scientific principle that forms the basis of the Tokamak technology is

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
${ }_{1}^{2} X +{ }_{1}^{2} X ={ }_{2}^{4} Y$
The binding energies per nucleon of ${ }_{1}^{2} X$ and ${ }_{2}^{4} Y$ are $1.1 \, MeV$ and $7.6 \, MeV$ respectively. The energy released in this process is in $MeV$.

Match the following items in Column-$A$ with their corresponding principles in Column-$B$:

Column-$A$	Column-$B$
$A$. Rocket propulsion	$P$. Bernoulli's principle in fluid dynamics
$B$. Aeroplane	$Q$. Total internal reflection of light
$C$. Optical fibres	$R$. Newton's laws of motion
$D$. Fusion test reactor	$S$. Magnetic confinement of plasma
	$T$. Photoelectric effect

The electrostatic energy of a nucleus of charge $Ze$ is equal to $\frac{k Z^2 e^2}{R}$,where $k$ is a constant and $R$ is the nuclear radius. The nucleus divides into two daughter nuclei of charges $\frac{Ze}{2}$ and equal radii. The change in electrostatic energy in the process when they are far apart is