The graph shows the variation with time of the activity of a radioactive sample,

The sample contains a radioactive element $\mathrm{X}$ that decays into a stable element $\mathrm{Y}$. At $\mathrm{t}=0$, no atoms of $\mathrm{Y}$  are in the sample present

in the sample. Determine the time after which the ratio of $\mathrm{Y}$ atoms to $\mathrm{X}$ atom is $7$

The intensity of gamma rays of specific energy (monochromatic rays) decreases exponentially with the thickness $\mathrm{x}$ of the absorbing material according to the equation

$\mathrm{I}={\mathrm{I}}_0{\mathrm{e}}^{-\mathrm{\mu x}}$   where $I_0$= intensity at the face of the absorber and $\mu$ is a constant depending upon the material

Discuss how the intensity $\mathrm{I}$ and thickness $\mathrm{x}$ should be plotted in order to allow an accurate determination of the constant $\mu$.

A fission reaction involving uranium is:

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{40}{}^{98}\mathrm{Zr}+{}_{52}{}^{135}\mathrm{Te}+3{}_0{}^1\mathrm{n}$

Calculate the energy released.(in $\mathrm{MeV}$) (Atomic masses: $\mathrm{U}=235.043922 \mathrm{u}$; $\mathrm{Zr}=97.91276 \mathrm{u}$; $\mathrm{Te}=134.9165 \mathrm{u}$)