Explanation

(a)
Four quantum numbers are
$n = 4,\ l = 0,\ m = 0,\ s = + \frac{1}{2}$
$n = 4$ indicates that the valence electron is present in 4th shell (4th period), $l = 0$ indicates that the valence electron is present in $s$-subshell. $m = 0$ indicates that the valence electron is present in orbital of $s$-subshell. $s = + \frac{1}{2}$ indicates that the spining of electron in orbital is clockwise. So, from the above discussion it is clear that valence electron is present in 4$s$ subshell as $4s^{1}.s^{1}$ indicates that the element is present in IA group. So, the element present in 4th period and IA group is potassium (K).