A heavy nucleus having mass number $200$ gets disintegrated into two small fragments of mass number $80$ and $120.$ If binding energy per nucleon for parent atom is $6.5 \mathrm{MeV}$ and for daughter nuclei is $7 \mathrm{MeV}$ and $8 \mathrm{MeV}$, respectively, then the energy released in the decay will be

When an electron accelerated by potential difference $U$ is bombarded on a specific metal, the emitted $X$-ray spectrum obtained is shown in adjoining graph. If the potential difference is reduced to $\frac{U}{3}\text{,}$ the correct spectrum is

A radioactive nuclide $A$ decays to nuclide $B$ which further decays to $C$. Their disintegration constant are ${\lambda }_1$ and ${\lambda }_2$, respectively. At $t=0$ only nuclei $A$ are present. Number of nuclei $A$ at $t=0$ is $N_0.$

$\begin{array}{cccc}& A\stackrel{{\lambda }_1}{⟶}& A\stackrel{{\lambda }_2}{⟶}& C\\ t=0& N_0& 0& 0\\ t& N_1& N_2& N_3\end{array}$

In the above radioactive decay $C$ is stable nucleus. Then

The radionuclide ${}^{238}\mathrm{U}$ decays by emitting an alpha particle.

${}^{236}\mathrm{U}\to {}^{234}\mathrm{Th}+{}^4\mathrm{He}$

The atomic masses of the three isotopes are.

${}^{234}\mathrm{U} 234.04363 \mathrm{amu}$

${}^4\mathrm{He} 4.00260 \mathrm{amu}$

What is the maximum kinetic energy of the emitted alpha particle? Express your answer in Joule $\left(1 \mathrm{amu}=1.67\times {10}^{-27} \mathrm{kg}\right)$