Find the average distance between the electron and proton in the Hydrogen ground-state. Use: <r> = ∫dr r*P(r) [bounds from 0 to +infinity: sorry I don't know how to properly type integrals] where ϕ(r) = Ae-r/aB is the ground-state solution of the radial Schrodinger equation for the Hydrogen atom (aB is Bohr's radius), and P(r) = 4πr2|ϕ(r)|2is the probability density that the electron would be located in the spherical shell between r and r + dr. First normalize the wavefunction to obtain the constant A: ∫dr P(r) = 1 [bounds from 0 to +infinity again]
Find the average distance between the electron and proton in the Hydrogen ground-state. Use: <r> = ∫dr r*P(r) [bounds from 0 to +infinity: sorry I don't know how to properly type integrals] where ϕ(r) = Ae-r/aB is the ground-state solution of the radial Schrodinger equation for the Hydrogen atom (aB is Bohr's radius), and P(r) = 4πr2|ϕ(r)|2is the probability density that the electron would be located in the spherical shell between r and r + dr. First normalize the wavefunction to obtain the constant A: ∫dr P(r) = 1 [bounds from 0 to +infinity again]
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Find the average distance between the electron and proton in the Hydrogen ground-state. Use:
<r> = ∫dr r*P(r)
[bounds from 0 to +infinity: sorry I don't know how to properly type integrals]
where ϕ(r) = Ae-r/aB is the ground-state solution of the radial Schrodinger equation for the Hydrogen atom (aB is Bohr's radius), and P(r) = 4πr2|ϕ(r)|2
is the probability density that the electron would be located in the spherical shell between r and r + dr. First normalize the wavefunction to obtain the constant A:
∫dr P(r) = 1
[bounds from 0 to +infinity again]
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