(a)
Given, X=[Ar]$d^{4}$
$\because\$The complete configuration of the ion,
$X^{3 +}\ = 1s^{2},\ 2s^{2}\ ,2p^{6},3s^{2}\ 3p^{6},3d^{4}$
$\therefore\ X = \ 1s^{2},\ 2s^{2}\ ,2p^{6},3s^{2},3p^{6}\ ,3d^{5}\ 4s^{2}$
$\therefore\$The atomic number of the element is 25 and the element is $Mn$.