Question

The radial probability distribution curve of an orbital of $H$ has $4$ local maxima. If the orbital has $3$ angular nodes, then the orbital will be

• A. 7f
• B. 8f
• C. 7d
• D. 8d

Answer 1

The correct option is A 7f

We know that,
Radial nodes is given by:
$n-l-1$
(a) For $7f$
$l=3$
i.e. n = 7
$n-l-1=7-3-1=3$
(b) For $8f$
$l=3,n=8$
$n-l-1=8-3-1=4$
(c) For $7d$
$d=2,n=7$
$n-l-1=7-2-1=4$
(d) For $8d$
$d=2,n=8$
$n-l-1=8-2-1=5$
As per the given question, there are $4$ local maxima in the radial distribution curve, so the orbital must have $3$ radial nodes.
Only $7f$ has $3$ radial nodes and according to the question the orbital has $3$ angular nodes, i.e., $l=3$, which means $f$ subshell. Hence, (a) is the correct answer.