Problem 1 For a Hydrogen atom in the ground state (and

Problem 1
For a Hydrogen atom in the ground state (and the approximation that the reduced mass = mass of an electron) the wavefunction is ?100 (r ? ?) = R10 (r) Y00 (? ?) where
R10 (r) = e-r/a0
and
Y00 (? ?) = (4p)-1/2
With ?100 (r) is possible to calculate the expectation values
100= (3/2) a0 100= 3a02
What is the uncertainty in the electron-nucleus distance for an Hydrogen atom in the ground state? Express it in terms of the Bohr radius a0=
What is the most probable value rmp for the distance between the electron and the nucleus?
What is the probability of finding the electron within a distance rmp-?r =r = rmp+?r from the nucleus?
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