ABC26PH0773 · Quantum Chemistry

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Particle In A Box · Exam: JAM 2001-2022 · Marks: 2 · Difficulty: Easy

(a) The electronic wavefunction $(\psi)$ for hydrogen atom in the 2 s state is given as
\[ \psi \propto\left(2-\frac{\mathrm{r}}{\mathrm{a}_{0}}\right) \exp \left(-\frac{\mathrm{r}}{2 \mathrm{a}_{0}}\right) \]
Determine the most probable radial distance for the electron in this state and also the position of the node (in terms of $\mathrm{a}_{0}$ ) (b) Calculate the wavelength corresponding to the lowest energy excitation of an electron confined to a one-dimensional box of length 1 nm. (Energy levels for a particle in a one dimensional box are given by $\mathrm{E}_{\mathrm{n}}=\mathrm{n}^{2} \mathrm{h}^{2} / 8 \mathrm{ma}^{2}$ ).
Answer
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Explanation
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