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).

When a sample of solid lithium is placed in a flask of hydrogen gas,the following reaction occurs: $_1^1H + {_3^7Li} \to {_2^4He} + {_2^4He}$. This statement is:

$_1H^1 + _1H^1 + _1H^2 \to X + _1e^0 + \text{Energy}$. The emitted particle $X$ is ........?

Assume that the nuclear binding energy per nucleon $(B/A)$ versus mass number $(A)$ is as shown in the figure. Use this plot to choose the correct choice$(s)$ given below:
$(A)$ Fusion of two nuclei with mass numbers lying in the range of $1 < A < 100$ will release energy.
$(B)$ Fusion of two nuclei with mass numbers lying in the range of $100 < A < 200$ will release energy.
$(C)$ Fission of a nucleus lying in the mass range of $100 < A < 200$ will release energy when broken into two equal fragments.
$(D)$ Fission of a nucleus lying in the mass range of $200 < A < 260$ will release energy when broken into two equal fragments.

If $200 \text{ MeV}$ of energy is released in the fission of one nucleus of ${ }_{92}^{236} U$, the number of nuclei that must undergo fission to release an energy of $1000 \text{ J}$ is

The rest mass of an electron as well as that of a positron is $0.51 \, MeV$. When an electron and a positron annihilate, they produce gamma-rays of wavelength(s):