The binding energy per nucleon of ${ }_5 B ^{10}$ is $8.0 \,MeV$ and that of ${ }_5 B ^{11}$ is $7.5 \,MeV$. The energy required to remove a neutron from ${ }_5 B ^{11}$ is .......... $MeV$.

Mass numbers of the elements $A, B, C$ and $D$ are $30, 60, 90$ and $120$ respectively. The specific binding energies of them are $5 \text{ MeV}, 8.5 \text{ MeV}, 8 \text{ MeV}$ and $7 \text{ MeV}$ respectively. In which of the following reaction$(s)$ is energy released?
$1. D \rightarrow 2B$
$2. C \rightarrow B + A$
$3. B \rightarrow 2A$

The mass of a nucleus,a neutron,and a proton are $M$,$M_n$,and $M_p$ respectively. Then which of the following is true?

If the speed of light were $2/3$ of its present value,the energy released in a given atomic explosion will be decreased by a fraction:

Write and explain Einstein's theory of special relativity in the context of mass-energy equivalence.

$A$ nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. The speed of light is $c$. The speed of the daughter nuclei is: