Question

Which of the following sets of quantum numbers represent electrons in a hydrogen atom?

• A. $1,1,0,+1/2$
• B. $1,0,0,+1/2$
• C. $3,0,0,-1/2$
• D. $4,2,1,-1/2$

Answer 1

The correct option is B

$1,0,0,+1/2$

The explanation for the correct option: (B)

1. The electron of a hydrogen atom is present in $1\mathrm{s}$ orbital and the value of the principal quantum number (n) is $1$.
2. The azimuthal quantum number $\left(\mathcal{l}\right)$ can have $0$ to $\text{n-1}$ values for a given value of ‘n’
3. The magnetic quantum number ( ${\mathrm{m}}_{\mathcal{l}}$) can have $-\mathcal{l}$ to $+\mathcal{l}$ including zero for a given value of $\left(\mathcal{l}\right)$.
4. The spin quantum number (s) can have any value of $\pm \frac{1}{2}$ as an electron can have any spin.
5. Thus the value of ‘n’ is $1$, $\mathcal{l}$ is $0$, ${\mathrm{m}}_{\mathcal{l}}$ is $0$ and s is $+\frac{1}{2}$.

The explanation for the incorrect options:

(A) The sets of quantum numbers represent electrons in a hydrogen atom is $1,0,0,+1/2$.

(C) The given set $3,0,0,-1/2$ does not represent the sets of quantum numbers for electrons in a hydrogen atom.

(D) The sets of quantum numbers represent electrons in a hydrogen atom are not $4,2,1,-1/2$.

Hence, option (B) is correct - The sets of quantum numbers represent electrons in a hydrogen atom is $1,0,0,+1/2$.