For the 2s orbital of a hydrogen atom, ψ ∝ (2 - r/a₀)e^(-r/2a₀), where a₀ = 52.9 pm. The chance of finding the electron in a thin spherical shell between r and r + dr is proportional to 4π r²ψ² dr. At what distance from the nucleus is this radial probability density largest?

ChemistryAdvancedHigh School (11–12)Structure of the Atom › Quantum Mechanical Model of the Atom JEE Advanced

For the $2s$ orbital of a hydrogen atom, $\psi \propto \left(2 - \dfrac{r}{a_0}\right)e^{-r/2a_0}$ , where $a_0 = 52.9\ \text{pm}$ . The chance of finding the electron in a thin spherical shell between $r$ and $r + dr$ is proportional to $4\pi r^2\psi^2\,dr$ . At what distance from the nucleus is this radial probability density largest?

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