Question

The maximum degenerate orbitals in the $3^{\mathrm{rd}}$ shell of ${\mathrm{Li}}^{2+}$ is

• A. $1$
• B. $5$
• C. $7$
• D. $9$

Answer 1

The correct option is D

$9$

Explanation for correct option

(d) 9

• Degenerate orbitals are those sorts of orbitals that have the same energy level as each other, i.e., they have no difference in energy levels.
• The atomic number of the Lithium atom is $3$ which means there are $3$ protons in the nucleus of the Lithium atom.
• $L{i}^{2+}$ state signifies that there is $1$ electron present in the atom only.
• The $3^{rd}$ shell means the M-shell where we have $3s,3p,3d$ sub-shells.
• Therefore the number of orbitals for each sub-shell will be, $s$ subshell having $1$ orbital, $p$ subshell having $3$ orbitals, and $d$ subshell with $5$ orbitals.
• Adding all these orbitals we get a sum of $9$ $\left(1+3+5=9\right)$.

Explanation for incorrect options

Since, the maximum degenerate orbitals in the $3^{\mathrm{rd}}$ shell of ${\mathrm{Li}}^{2+}$ is 9. Therefore, options (a), (b) and (c) are incorrect.

Hence, option (d) is correct.