Question

Which of the following is a correct set of four quantum numbers for 4d orbital?

• A. $(4, 3, 2, +1/2)$
• B. $(4, 2, 1, +1/2)$
• C. $(4, 1, 2, +1/2)$
• D. None of these

Hint:

Remember the s-p-d-f sequence for $l$: $s=0, p=1, d=2, f=3$.

Answer 1

The Correct Option is B

Step 1: Concept
Quantum numbers describe the state of an electron. For a $4d$ orbital:
$n$ (principal quantum number) $= 4$
$l$ (azimuthal quantum number) for $d$ orbitals is always $2$.

Step 2: Meaning
The rules for quantum numbers are:
$l$ ranges from $0$ to $n-1$.
$m_{l}$ (magnetic quantum number) ranges from $-l$ to $+l$.
$s$ (spin quantum number) is either $+1/2$ or $-1/2$.

Step 3: Analysis
For $4d$: $n=4$ and $l=2$.
Option (A): $l=3$ (This refers to a $4f$ orbital).
Option (B): $n=4, l=2$. Here $m=1$ is valid because $-2 \leq m \leq 2$.
Option (C): $l=1$ (This refers to a $4p$ orbital).

Step 4: Conclusion
Only option (B) correctly identifies the $n$ and $l$ values for a $4d$ orbital while maintaining valid $m$ and $s$ values. Final Answer: (B)