$A$ certain radioactive nuclide of mass number $m_x$ disintegrates,with the emission of an electron and $\gamma$ radiation only,to give a second nuclide of mass number $m_y$. Which one of the following equations correctly relates $m_x$ and $m_y$?

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

$A$ radio nuclide $A_1$ with decay constant $\lambda_1$ transforms into a radio nuclide $A_2$ with decay constant $\lambda_2$. If at the initial moment the preparation contained only the radio nuclide $A_1$,then the time interval after which the activity of the radio nuclide $A_2$ reaches its maximum value is:

In the Uranium radioactive series,the initial nucleus is ${ }_{92}^{238} U$ and the final nucleus is ${ }_{82}^{206} Pb$. When the Uranium nucleus decays to lead,the number of $\alpha$-particles emitted is .......... and the number of $\beta$-particles emitted is ..........

$A$ nucleus of atomic mass $A$ and atomic number $Z$ emits a $\beta^-$ particle. The atomic mass and atomic number of the resulting nucleus are

In a radioactive reaction $_{92}X^{232} \to _{82}Y^{204}$,the number of $\alpha$-particles emitted is: