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What is the overage strength of the nucleus of H- - - tom for the given normalized wove function?
$\psi_{2,0,0}=\frac{1}{\sqrt{32 \pi}}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left(2-\frac{r}{a_{0}}\right) e^{-r / 2 a_{0}}$
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Answer from Sia

Posted 2 months ago

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Answer

The average strength of the nucleus of the hydrogen atom for the given normalized wave function is $-\frac{e^2}{8 \pi \epsilon_0 a_0}$.

Key Concept

Expectation value of potential energy

Explanation

The expectation value of the potential energy for a given wave function provides the average strength of the nucleus in a hydrogen atom. For the $2s$ state, this involves integrating the potential energy function with the square of the wave function.

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