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.

Answer 1

1. The general valence electronic configuration of an inert gas is ${\mathrm{ns}}^2{\mathrm{np}}^6$.
2. The total of the valence electron's four quantum numbers in an inert gas is the total of the principal quantum numbers$=8\times \mathrm{n}$
3. Azimuthal quantum number sum$=(2\times 0)+$ $(6\times 1)$
4. Magnetic quantum numbers added together $=0$
5. Quantum spin numbers added together $=0$
   $\therefore 8\mathrm{n}+6=22$

$\therefore \mathrm{n}=\frac{16}{8}=2$

6. The inert gas's electrical configuration of valence is $2{\mathrm{s}}^{2}2{\mathrm{p}}^6$ As a result, neon is the inert gas..