The intensity of gamma radiation emitted from a source is $I_0$. After passing through a lead sheet of thickness $36 \, mm$,its intensity becomes $I_0/8$. Find the thickness of the lead sheet in $mm$ when the intensity becomes $I_0/2$.

For the $\beta^{+}$ (positron) emission from a nucleus,there is another competing process known as electron capture (an electron from an inner orbit,say,the $K$-shell,is captured by the nucleus and a neutrino is emitted).
$_{z}^{A} X + e^{-} \rightarrow _{z-1}^{A} Y + \nu$
Show that if $\beta^{+}$ emission is energetically allowed,electron capture is necessarily allowed,but not vice-versa.

Which of the following can penetrate through an aluminum sheet of $20 \, cm$ thickness?

$A$ radioactive nucleus undergoes $\alpha$-emission to form a stable element. What will be the recoil velocity of the daughter nucleus if $V$ is the velocity of $\alpha$-emission and $A$ is the atomic mass of the radioactive nucleus?

$A$ nucleus ${ }_{Z} X^{A}$ emits an $\alpha$-particle with velocity $v$. The recoil speed of the daughter nucleus is

$37$ Rutherford equals