$A$ nucleus with $Z = 92$ emits $\alpha, \alpha, \beta^-, \beta^-, \alpha, \alpha, \alpha, \alpha, \beta^-, \beta^-, \alpha, \beta^+, \beta^+, \alpha$ particles in sequence. What is the $Z$ of the resulting nucleus?

The intensity of gamma rays is reduced to half when they pass through a lead sheet of thickness $2.5 \, mm$. The absorption coefficient of lead is ......... $mm^{-1}$.

An atomic nucleus $_{90}^{232}Th$ emits several $\alpha$ and $\beta$ radiations and finally reduces to $_{82}^{208}Pb$. It must have emitted:

In a radioactive decay,an element $^A_Z X$ emits four $\alpha$-particles,three $\beta$-particles and eight $\gamma$-photons. The atomic number and mass number of the resulting final nucleus are

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.

$A$ radioactive element forms its own isotope after $3$ consecutive disintegrations. The particles emitted are