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

An $U^{238}$ nucleus is initially at rest. It decays by emitting an $\alpha$-particle with speed $u$. Find the recoil speed of the daughter nucleus.

$A$ nucleus $_Z{X^A}$ emits $9 \alpha$-particles and $5 \beta$-particles. The ratio of total protons to neutrons in the final nucleus is:

$A$ nucleus $_Z{X^A}$ emits $3 \alpha$-particles and $5 \beta$-particles. The ratio of total neutrons to protons in the final nucleus is:

$A$ radioactive nucleus decays as follows:
$X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4$
If the atomic number and the mass number of $X$ are $72$ and $180$ respectively,then the mass number and atomic number of $X_4$ are:

$A$ nucleus $X$ emits a beta particle to produce a nucleus $Y$. If their atomic masses are $M_{x}$ and $M_{y}$ respectively,the maximum energy of the beta particle emitted is (where $m_{e}$ is the mass of an electron and $c$ is the velocity of light):