Question

Which of the following sets of quantum numbers is correct for an electron in 3d-orbital?

• A. $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-3,\mathrm{s}=+\frac{1}{2}$
• B. $\mathrm{n}=3,\mathrm{l}=3,\mathrm{m}=+3,\mathrm{s}=-\frac{1}{2}$
• C. $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-2,\mathrm{s}=+\frac{1}{2}$
• D. $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-3,\mathrm{s}=-\frac{1}{2}$

Answer 1

The correct option is C

$\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-2,\mathrm{s}=+\frac{1}{2}$

Explanation for the correct option:

C) $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-2,\mathrm{s}=+\frac{1}{2}$

• $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-2,\mathrm{s}=+\frac{1}{2}$ are the sets of quantum numbers for an electron in 3d-orbital.
• The principal quantum number (n) represents the shell number. So, the n value for 3d orbital is $3$.
• Angular quantum number (l) for s,p,d and f orbitals is $\mathrm{l}=0,1,2,3$respectively. Hence the l for 3d orbital is $2$.
• The magnetic quantum number (m) is dependent on the value of the angular quantum number (l). For a given value of l, the value of m ranges between the interval -l to +l. Therefore, it indirectly depends on the value of n. So the m value for 3d orbital ranges from $-2\mathrm{to}+2$.
• The spin quantum number(s) is always $+\frac{1}{2}$or $-\frac{1}{2}$

Explanation for the incorrect options:

A) $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-3,\mathrm{s}=+\frac{1}{2}$

• $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-3,\mathrm{s}=+\frac{1}{2}$ are not the sets of quantum numbers for an electron in 3d-orbital.
• Since the l value for 3d orbital is $2$, the m value for 3d orbitals are $-2,-1,0,+1,+2$. So the given value of m =$-3$ is not correct.

B) $\mathrm{n}=3,\mathrm{l}=3,\mathrm{m}=+3,\mathrm{s}=-\frac{1}{2}$

• $\mathrm{n}=3,\mathrm{l}=3,\mathrm{m}=+3,\mathrm{s}=-\frac{1}{2}$ are not the sets of quantum numbers for an electron in 3d-orbital.
• l value for s,p,d and f orbitals is $\mathrm{l}=0,1,2,3$ respectively. So, the l value for the d orbital is $2$, not $3$.
• Since the l value for 3d orbital is $2$, the m value for 3d orbitals are $-2,-1,0,+1,+2$. So the given value of m = $+3$ is not correct.

D) $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-3,\mathrm{s}=-\frac{1}{2}$

• $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-3,\mathrm{s}=-\frac{1}{2}$ are not the sets of quantum numbers for an electron in 3d-orbital.
• Since the l value for 3d orbital is $2$, the m value for 3d orbitals are $-2,-1,0,+1,+2$. So the given value of m =$-3$ is not correct.

Hence, option (C) is correct i.e. $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=-2,\mathrm{s}=+\frac{1}{2}$