Calculate the most probable value of r for an electron in a hydrogen 1s orbital.

Expert Solution

The radial probability density for the hydrogen ground state is obtained by multiplying the square of the wavefunction by a spherical shell volume element.

It takes this comparatively simple form because the 1s state is spherically symmetric and no angular terms appear.

Dropping off the constant terms and taking the derivative with respect to r and setting it equal to zero gives the radius for maximum probability.

which gives

where

queen_honey_blossom answered 2 years ago

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