Question

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

Explanation:

Step1: Recall the relationship between \(n\) and \(l\)

The principal quantum number \(n\) and the angular - momentum quantum number \(l\) satisfy the relation \(l = 0,1,\cdots,n - 1\). For a \(d\) electron, \(l=2\).

Step2: Determine the minimum value of \(n\)

Since \(l = 2\) and \(l\leq n - 1\), then \(n-1\geq2\). Solving the inequality \(n-1\geq2\) gives \(n\geq3\).

Answer:

\(n = 3\)