Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Hydrogen Atom · Exam: JAM 2001-2022 · Marks: 2 · Difficulty: Medium
An atomic orbital is described by the wavefunction $\psi(\mathrm{r})=\frac{1}{\sqrt{\pi \mathrm{a}_{0}^{3}}} \mathrm{e}^{-\left(\frac{\mathrm{r}}{\mathrm{a}_{0}}\right)}$, where $\mathrm{a}_{0}$ is the Bohr radius. Given: $\mathrm{d} \tau=\mathrm{r}^{2} \sin \theta \mathrm{drd} \theta \mathrm{d} \phi$ and $\int_{0}^{\infty} \mathrm{r}^{\mathrm{n}} \mathrm{e}^{-\beta \mathrm{r}} \mathrm{d} \tau=\frac{\mathrm{n}!}{\beta^{\mathrm{n}+1}}$ (n is a positive integer)(a) Identify the atomic orbital and calculate the mean or the average radius of this orbital in terms of $\mathrm{a}_{0}$.(b) Calculate the most probable radius (in terms of $\mathrm{a}_{0}$ ) at which an electron will be found when it occupies this orbital.
Answer
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