$\alpha$-decay of a parent nucleus $X$ results in a daughter nucleus $Y$. If $m_x, m_y$ and $m_a$ are the masses of the parent nucleus,the daughter nucleus and the $\alpha$-particle respectively,then the net kinetic energy gained in the process is:

Actinium $231$,${}^{231}Ac_{89}$,emits in succession two $\beta^-$ particles,four $\alpha$ particles,one $\beta^-$ particle,and one $\alpha$ particle,plus several $\gamma$ rays. What is the resultant isotope?

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?
$(A)$ $N_{\alpha}=5$
$(B)$ $N_{\alpha}=6$
$(C)$ $N_{\beta}=2$
$(D)$ $N_{\beta}=4$

In the uranium radioactive series,the initial nucleus ${}^{238}_{92}U$ decays to the final nucleus ${}^{206}_{82}Pb$. In this process,the number of $\alpha$-particles and $\beta$-particles emitted are:

$A$ radioactive substance emits

$\beta$-decay means emission of electron from