The Coulombic potential operator for the electron in the hydrogen atom is: V(r) = 4πer Calculate the average value of the potential energy for an electron in a 1s orbital with the vavefunction (note the use of spherical coordinates): √ (r, 0, 0). = πα

The Coulombic potential operator for the electron in the hydrogen atom is: V(r) = 4πer Calculate the average value of the potential energy for an electron in a 1s orbital with the vavefunction (note the use of spherical coordinates): √ (r, 0, 0). = πα

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Question

The Coulombic potential operator for the electron in the hydrogen atom is:
ŷ(r) =
4πer
Calculate the average value of the potential energy for an electron in a 1s orbital with the
wavefunction (note the use of spherical coordinates):
(r, 0, 0) =
√5
Fe
πα,

Expert Solution

Step 1: Step 1

$Given space that colon straight V with hat on top equals fraction numerator negative straight e squared over denominator 4 straight pi straight epsilon subscript straight o straight r end fraction straight psi left parenthesis straight r comma straight theta comma straight ϕ right parenthesis equals square root of 1 over straight pi straight a subscript straight o cubed end root straight e to the power of negative straight r over straight a subscript straight o end exponent$

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