The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}^{16} \mathrm{~N}+$ ${ }_{2}^{4} \mathrm{He} \rightarrow{ }_{1}^{1} \mathrm{H}+{ }_{8}^{19} \mathrm{O}$ in a laboratory frame is $n$ (in $M e V$. Assume that ${ }_{7}^{16} \mathrm{~N}$ is at rest in the laboratory frame. The masses of ${ }_{7}^{16} \mathrm{~N},{ }_{2}^{4} \mathrm{He},{ }_{1}^{1} \mathrm{H}$ and ${ }_{8}^{19} \mathrm{O}$ can be taken to be $16.006 u, 4.003 u, 1.008 u$ and $19.003 u$, respectively, where $1 u=930 \,\mathrm{MeVc}^{-2}$. The value of $n$ is ________ .

Suppose a $$_{88}^{226}Ra$$ nucleus at rest and in ground state undergoes $$\alpha $$-decay to a $$_{86}^{222}Rn$$ nucleus in its excited state. The kinetic energy of the emitted $$\alpha $$ particle is found to be 4.44 MeV. $$_{86}^{222}Rn$$ nucleus then goes to its ground state by $$\gamma $$-decay. The energy of the emitted $$\gamma $$ photon is ............ keV.

[Given : atomic mass of $$_{86}^{226}Ra$$ = 226.005 u, atomic of $$_{86}^{222}Rn$$ = 222.000 u, atomic mass of $$\alpha $$ particle = 4.000 u, 1 u = 931 MeV/e², c is speed of the light]

Consider a hydrogen-like ionized atom with atomic number $$Z$$ with a single electron. In the emission spectrum of this atom, the photon emitted in the $$n=2$$ to $$n=1$$ transition has energy $$74.8eV$$ higher than the photon emitted in the $$n=3$$ to $$n=2$$ transition. The ionization energy of the hydrogen atom is $$13.6$$ $$eV.$$ The value of $$Z$$ is ____________.

$${}^{131}{\rm I}$$ is an isotope of Iodine that $$B$$ decays to an isotope of Xenon with a half-life of $$8$$ days. A small amount of a serum labelled with $${}^{131}{\rm I}$$ is injected into the blood of a person. The activity of the amount of $${}^{131}{\rm I}$$ injected was $$2.4 \times {10^5}$$ Becquerel $$(Bq).$$ It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After $$11.5$$ hours, $$2.5$$ ml of blood is drawn from person's body, and gives an activity of $$115$$ $$Bq$$. The total volume of blood in the person's body, in liters is approximately (you may use $${e^x} \approx 1 + x\,\,$$ for $$\left| x \right| < < 1$$ and $$\ln 2 \approx 0.7).$$