Question

The maximum number of electrons in a sub-shell is

• A. $2(2l+1)$
• B. $2l+1$
• C. $2l$
• D. $2l-1$

Answer 1

The correct option is A $2(2l+1)$

We know that the first shell consists of only s orbital i.e. 1 subshell and can accommodate 2 electrons. The second shell consists of two orbitals namely s and p and it can accommodated 2 electrons in the s orbital and 6 electrons in the p orbital i.e. a total of 8 electrons in the second shell.
Likewise, the d subshell accommodates 10 electrons and f subshell accommodates 14 electrons.
Thus we see that the maximum electrons in any subshell is given using $2(2l+1).$
For $l=0$ we have $n=2$
For $l=1$ we have $n=6$
For $l=2$ we have $n=10$
For $l=3$ we have $n=14$
($l$ is the azimuthal quantum number)