$A$ nucleus with mass number $220$ initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is $5.5\, MeV$,calculate the kinetic energy of the $\alpha$-particle in $MeV$.

In a radioactive decay chain,${ }_{90}^{232} Th$ nucleus decays to ${ }_{82}^{212} Pb$ nucleus. Let $N_{\alpha}$ and $N_{\beta}$ be the number of $\alpha$ and $\beta^{-}$ particles,respectively,emitted in this decay process. Which of the following statements is (are) true?
$(A)$ $N_{\alpha}=5$
$(B)$ $N_{\alpha}=6$
$(C)$ $N_{\beta}=2$
$(D)$ $N_{\beta}=4$

When $_{90}^{228}Th$ transforms to $_{83}^{212}Bi$,the number of emitted $\alpha$- and $\beta$- particles is,respectively:

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.

The radioactive nucleus $_7N^{13}$ decays to $_6C^{13}$ through the emission of

In radioactive decay process,the negatively charged emitted $\beta$-particles are