$A$ radioactive nucleus of mass number $A$, initially at rest, emits an $\alpha$-particle with a speed $v$. The recoil speed of the daughter nucleus will be

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is
$^{38}S \xrightarrow{2.48 \ h} ^{38}Cl \xrightarrow{0.62 \ h} ^{38}Ar$
Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38}Cl$ nuclei is zero at $t = 0$ and will again be zero at $t = \infty$. At what value of $t$ would the number of $^{38}Cl$ nuclei be a maximum?

After the decay of a single $\beta$ particle, the parent and daughter nuclei are

$A$ radioactive decay chain starts from $_{93}Np^{237}$ and produces $_{90}Th^{229}$ by successive emissions. The emitted particles can be:

In which of the following decay processes does the element not change?

In $\beta^{-}$ decay, a neutron transforms into a proton within the nucleus according to the equation:
$\text{neutron} \rightarrow \text{proton} + \beta^{-} + x$
In this equation, the particle represented by '$x$' is: