Question

If Azimuthal quantum number has possible values from $0$ to $n+1$ and there are $3$ possible values for spin quantum number $(+\frac{1}{2},0,-\frac{1}{2})$, then maximum number of electrons which can be filled into $3$rd orbit are:

• A. $25$
• B. $50$
• C. $75$
• D. $100$

Answer 1

The correct option is C $75$

Given, Azimuthal quantum number $\left(l\right)$ can have values from $0$ to $n+1$.
Here we are considering $3$rd orbit, so $n=3$
$\therefore l=0,1,2,3,4$
So, possible magnetic quantum number values $\left(m_l\right)$ are
$0,(-1,0,+1),(-2,-1,0,+1,+2),(-3,-2,-1,0,+1,+2,+3),(-4,-3,-2,-1,0,+1,+2,+3,+4)$
So, total $25$ orbital in $3$rd orbit and each orbital can have $3$ electrons as spin quantum number has $3$ possible values.
Thus maximum possible number of electrons in $3$rd orbit would be $25\times 3=75$.