Question

The sum of all the quantum numbers of all the valence electrons of an atom of an inert gas is 22. Identify the inert gas:

• A. Helium
• B. Neon
• C. Argon
• D. Krypton

Answer 1

Answer: (B)

Neon

Let $n{s}^{2}n{p}^6$ be the valence electronic configuration of inert gas.
Sum of the principal quantum numbers $=8n$
Sum of azimuthal quantum numbers $=(2\times 0)+(6\times 1)$
Sum of magnetic quantum numbers $=0$
Sum of spin quantum numbers $=0$
The sum of all the quantum numbers of all the valence electrons of an atom of an inert gas is 22.
$8n+6=22$
$n=2$
Valence electronic configuration of inert gas is $2s^{2}2p^6$
The inert gas is neon.