In the process of a nuclear explosion,in which form is the maximum energy released?

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

In a reactor, $2 \, kg$ of ${ }_{92} U ^{235}$ fuel is fully used up in $30$ days. The energy released per fission is $200 \, MeV$. Given that the Avogadro number, $N_A = 6.023 \times 10^{26} \, \text{per kilo mole}$ and $1 \, eV = 1.6 \times 10^{-19} \, J$. The power output of the reactor is close to $..... \, MW$.

The mass of a nucleus ${ }_Z^A X$ is less than the sum of the masses of $(A-Z)$ neutrons and $Z$ protons. The energy equivalent to this mass difference is the binding energy. $A$ heavy nucleus of mass $M$ can break into two light nuclei of masses $m_1$ and $m_2$ only if $M > (m_1+m_2)$. The masses of some neutral atoms are given in the table below:

${ }_1^1 H$: $1.007825 u$	${ }_1^2 H$: $2.014102 u$	${ }_1^3 H$: $3.016050 u$	${ }_2^4 He$: $4.002603 u$
${ }_3^6 Li$: $6.015123 u$	${ }_3^7 Li$: $7.016004 u$	${ }_{30}^{70} Zn$: $69.925325 u$	${ }_{34}^{82} Se$: $81.916709 u$
${ }_{64}^{152} Gd$: $151.919803 u$	${ }_{82}^{206} Pb$: $205.974455 u$	${ }_{83}^{209} Bi$: $208.980388 u$	${ }_{84}^{210} Po$: $209.982876 u$

$1.$ The correct statement is:
$(A)$ The nucleus ${ }_3^6 Li$ can emit an alpha particle.
$(B)$ The nucleus ${ }_{84}^{210} Po$ can emit a proton.
$(C)$ Deuteron $({ }_1^2 H)$ and alpha particle $({ }_2^4 He)$ can undergo complete fusion.
$(D)$ The nuclei ${ }_{30}^{70} Zn$ and ${ }_{34}^{82} Se$ can undergo complete fusion.
$2.$ The kinetic energy (in $keV$) of the alpha particle, when the nucleus ${ }_{84}^{210} Po$ at rest undergoes alpha decay, is:
$(A)$ $5319$ $(B)$ $5422$ $(C)$ $5707$ $(D)$ $5818$

In an $\alpha -$ decay,the kinetic energy of the $\alpha -$ particle is $48 \ MeV$ and the $Q$ value of the reaction is $50 \ MeV$. The mass number of the mother nucleus is (assume that the daughter nucleus is in the ground state).

Calculate the height of the potential barrier for a head-on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius $2.0 \; fm$.)