Which of the following is true for the radial part of the hydrogen atom wave functions $\mathrm{R}_{\mathrm{n} 1}(\mathrm{r})$ ( n principal quantum number) and the nodes associated with them?
(a)The radial part of only s function is non-zero at the origin and has ($\mathrm{n}-1$) nodes.
(c)All radial functions have values of zero at the origin and have ( $\mathrm{n}-1$ ) nodes.
(d)The radial parts of all s functions are zero at the origin and have no nodes.
Answer
Answer: A ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
R_nl(r) ∝ r^l near the origin, so only s functions (l = 0) are non-zero at r = 0; an ns radial function has n − l − 1 = n − 1 nodes.