We need electrons in all completely filled subshells with:

• principal quantum number $n=4$
• spin quantum number $s=+\frac{1}{2}$

For $n=4$, the possible subshells are: $4s,\;4p,\;4d,\;4f$ because for a given $n$, $l=0,1,2,3$.

A completely filled subshell contains the maximum allowed electrons:

• $s$ subshell: $2$ electrons
• $p$ subshell: $6$ electrons
• $d$ subshell: $10$ electrons
• $f$ subshell: $14$ electrons

But the question asks only for electrons with spin quantum number $s=+\frac{1}{2}$ In a completely filled subshell, half the electrons have spin $+\frac{1}{2}$ and half have spin $-\frac{1}{2}$.

Therefore, number of electrons with spin $+\frac{1}{2}$ in each filled subshell:

• $4s$: $\frac{2}{2}=1$
• $4p$: $\frac{6}{2}=3$
• $4d$: $\frac{10}{2}=5$
• $4f$: $\frac{14}{2}=7$

Total number of such electrons: $1+3+5+7=16$

Hence, the required number of electrons is: $\boxed{16}$

Comparison with stored correct answer:

• Stored correct answer = $16$
• Derived answer = $16$
• They match.