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## Main Question or Discussion Point

I am trying to prove to myself that the most probable distance for a 1s electron in a H atom is the Bohr radius.

The probability of finding an electron (for any given state in a hydrogenic atom) in a spherical shell of thickness dr at a distance r from the nucleus is [itex]\left|R_{nl}\right|^{2} r^{2} dr = \left|\psi_{nlm}\right|^{2} 4\pi r^{2} dr [/itex].

Given this, I need to differentiate this expression wrt r to obtain the radius at which the radial probability is maximum. This is where I face the problem. How do I differentiate either of the above expressions when there's a dr in each of them?

The probability of finding an electron (for any given state in a hydrogenic atom) in a spherical shell of thickness dr at a distance r from the nucleus is [itex]\left|R_{nl}\right|^{2} r^{2} dr = \left|\psi_{nlm}\right|^{2} 4\pi r^{2} dr [/itex].

Given this, I need to differentiate this expression wrt r to obtain the radius at which the radial probability is maximum. This is where I face the problem. How do I differentiate either of the above expressions when there's a dr in each of them?