(a) Calculate ((1/|r 1 - r 2 |)) for the state 0 (Equation 5.41). Do the d...

(a) Calculate ((1/|r₁ - r₂|)) for the state Ψ0 (Equation 5.41). Do the d³r₂ integral first, using spherical coordinates, and setting the polar axis along r₁, so that

The θ₂ integral is easy, but be careful to take the positive root. You’ll have to break the r₂ integral into two pieces, one ranging from 0 to r₁, the other from to r₁ to ∞.
(b) Use your result in (a) to estimate the electron interaction energy in the ground state of helium. Express your answer in electron volts, and add it to E₀ (Equation 5.42) to get a corrected estimate of the ground state energy. Compare the experimental value. (Of course, we’re still working with an approximate wave function, so don’t expect perfect agreement.)

Equation 5.41

Equation 5.42

Transcribed Image Text:

1₁ - 12| = √√²+² - 2112 cos 02.