The electron emitted in beta radiation originates from

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

$A$ nucleus decays by ${\beta ^ + }$ emission followed by a gamma emission. If the atomic and mass numbers of the parent nucleus are $Z$ and $A$ respectively, the corresponding numbers for the daughter nucleus are respectively.

$A$ radioactive element $A$ decays into radioactive element $C$ by the following processes in succession.
$A \rightarrow B + {}_{2}^{4}He$
$B \rightarrow C + 2e^{-}$
Then elements

Which of the following processes represents a gamma-decay?

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?