Question

In a hypothetical atom, the number of electrons in shell and subshell are $x$ and $y$, respectively, where each electron has three possible spin states represented as $s=+1/2,-1/2$ and $0$.
Then the value of $x+y$ is:

• A. $2n^2+4l+2$
• B. $3n^2+3l+1$
• C. $3n^2+6l+3$
• D. $6n^2+3l+3$

Answer 1

The correct option is C $3n^2+6l+3$

$1$ subshell has $(2l+1)$ orbitals .

Each orbital has $3$ electrons.

$\therefore y=(2l+1)\times 3=6l+3$

Each shell has $n^2$ orbitals.

$\therefore x=3n^2$

$\therefore x+y=3n^2+6l+3$