Question

How many orbitals in total are associated with $4^{th}$ energy level?

• A. 4
• B. 9
• C. 16
• D. 7

Answer 1

The correct option is C 16

For $4^{th}$ energy level, $n=4$ and possible values of l and $m_l$ are:

$l=0,1,2,3$

$m_l=0$ for $l=0$; total $m_l$ values $=1$

$m_l=-1,0,1$ for $l=1$; total $m_l$ values $=3$

$m_l=-2,-1,0,1,2$ for $l=2$; total $m_l$ values $=5$

$m_l=-3,-2,-1,0,1,2,3$ for $l=3$; total $m_l$ values $=7$

Total number of orbitals $=$ total values of $m_l$

For $n=4$,

$\therefore 1+3+5+7=16$ orbitals present in $4^{th}$ energy level.

Hence, option $C$ is correct.