Consider the radioactive decay: $.$

a$)$ What particles are included in the decay product X$?[1]$

b$)$ Using the masses of neutral atoms of $23$Mg $(22\mathrm{.}994124$ u$)$ and $23$Na $(22\mathrm{.}989769$ u$),$

show that the decay is energetically possible. $[2]$

c$)$ Calculate the maximum kinetic energy of the charged particle $($not the nucleus$)$

emitted in the decay and its maximum velocity. $($Ignore the small kinetic energy of the

nucleus.$)[3]$

d$)$ The half$-$life of $23$Mg is $11\mathrm{.}317$ s$.$ How long it will take for $90\%$ of original nuclei

of $23$Mg to decay? $[2]$

$$

$12$

$23$ Mg $11$

$23$Na $+$ X