Which of the following statement concerning probability density (ψ2) and radial distribution function (4πr2ψ2) for a s-orbital of H-like species is correct?

# Which of the following statement concerning probability density (${\mathrm{\psi }}^{2}$) and radial distribution function (4$\mathrm{\pi }$r2${\mathrm{\psi }}^{2}$) for a s-orbital of H-like species is correct?

1. A

${\mathrm{\psi }}^{2}$ is minimum at nucleus but 4${\mathrm{\pi r}}^{2}$ ${\mathrm{\psi }}^{2}$ is maximum at nucleus

2. B

${\mathrm{\psi }}^{2}$ is maximum at nucleus but 4${\mathrm{\pi r}}^{2}$ ${\mathrm{\psi }}^{2}$ is minimum at nucleus.

3. C

Both ${\mathrm{\psi }}^{2}$ and 4${\mathrm{\pi r}}^{2}$ ${\mathrm{\psi }}^{2}$ are maximum at nucleus.

4. D

Both ${\mathrm{\psi }}^{2}$ and 4${\mathrm{\pi r}}^{2}$ ${\mathrm{\psi }}^{2}$ are minimum at nucleus.

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### Solution:

$\mathrm{\psi }=\frac{1}{\sqrt{\mathrm{\pi }}}{\left(\frac{1}{{\mathrm{a}}_{0}}\right)}^{3/2}={\mathrm{e}}^{\left(-\frac{\mathrm{r}}{{\mathrm{a}}_{0}}\right)}$
Hence, ${\mathrm{\psi }}^{2}$ is maxirnum at r = 0, but 4${\mathrm{\pi r}}^{2}$ ${\mathrm{\psi }}^{2}$ is minimum at r = 0.

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