Question

Among the following, the orbital that has the lowest energy is

• A. $5\mathrm{f}$
• B. $4\mathrm{f}$
• C. $6\mathrm{s}$
• D. $6\mathrm{p}$

Answer 1

The correct option is C

$6\mathrm{s}$

The explanation for the correct option: (C)

1. The energy of an orbital depends upon the sum of the values of the principal quantum number (n) and the azimuthal quantum number (l).
2. The orbital with the lower value of $(\text{n}+\text{l)}$ has lower energy.
3. The value of the azimuthal quantum number for $\text{'}\mathrm{f}\text{'}$ orbital is $3$, for $\text{'}\mathrm{s}\text{'}$ orbital it is $0$ and for $\text{'}\mathrm{p}\text{'}$orbital it is $1$.
4. The $(\text{n+l)}$ values of $5\mathrm{f}$ orbital is $8$, for $4\mathrm{f}$ orbital it is $7$, for $6\mathrm{s}$ orbital it is $6$ , and for $6\mathrm{p}$ orbital it is $7$.
5. Thus $6\mathrm{s}$ orbital has lower energy.

The explanation for the incorrect options:

(A) The orbital that has the lowest energy is $6\mathrm{s}$ not $5\mathrm{f}$.

(B) It is $6\mathrm{s}$ orbital that has the lowest energy not $4\mathrm{f}$ orbital.

(D) The orbital that has the lowest energy is $6\mathrm{s}$ not $6\mathrm{p}$.

Hence, option (C) is correct - The orbital that has the lowest energy is $6\mathrm{s}$.