Question

A certain orbital has $\mathrm{n}=4$ and ${\mathrm{m}}_l=-3$.The number of radial nodes in the orbital is__________. (Round off to the nearest integer)

Answer 1

Answer: 0

$$\begin{gathered} \mathrm{Given}:\mathrm{n}=4 \\ {\mathrm{m}}_{\mathrm{l}}=(-3) \\ {\mathrm{m}}_l=(-\mathrm{l})\mathrm{to}+\mathrm{l} \\ \mathrm{l}=0\to {\mathrm{m}}_l=0 \\ \mathrm{l}=1\to {\mathrm{m}}_l=(-1),0,(+1) \\ \mathrm{l}=2\to {\mathrm{m}}_l=(-2),(-1),0,(+1),(+2) \\ \mathrm{l}=3\to {\mathrm{m}}_l=(-3),(-2),(-1),0,(+1),(+2),(+3) \\ \mathrm{Hence}, \\ \mathrm{l}=3 \\ \mathrm{Number}\mathrm{of}\mathrm{radial}\mathrm{nodes}=\mathrm{n}-\mathrm{l}-1 \\ =4-3-1 \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0} \end{gathered}$$