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 $I_0/2$.

$A$ radioactive element emits two $\beta$-particles and one $\alpha$-particle. The resulting daughter nucleus is ...

If $_{92}U^{238}$ undergoes successively $8 \alpha$-decays and $6 \beta$-decays,then the resulting nucleus is

In the disintegration series
$_{92}^{238}U \xrightarrow{\alpha} X \xrightarrow{\beta} _{Z}^{A}Y$
The values of $Z$ and $A$ respectively will be:

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)

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.