(a) The electronic wavefunction (ψ) for hydrogen atom in the 2s state is given as ψ ∝ (2 - r/(a₀))exp… · ABC26PH0773

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 2s state is given as
$\psi \propto \left(2 - \frac{r}{a_0}\right)\exp\left(-\frac{r}{2a_0}\right)$
Determine the most probable radial distance for the electron in this state and also the position of the node (in terms of $a_0$)
(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 $E_n = n^2h^2/8ma^2$).
Answer
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Explanation
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