Question

what is the smallest possible value of the principal quantum number n for a d electron?

Explanation:

Step1: Recall quantum - number rules

The angular - momentum quantum number $l$ for a $d$ electron is $l = 2$.
The relationship between the principal quantum number $n$ and the angular - momentum quantum number $l$ is $l=0,1,\cdots,n - 1$.

Step2: Determine the minimum $n$

Since $l = 2$, from the inequality $l\leq n - 1$, we can solve for $n$. Rearranging gives $n\geq l + 1$. Substituting $l = 2$ into the inequality, we get $n\geq3$. So the smallest value of $n$ is 3.

Answer:

3