Quantum Chemistry

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Exercise. This is the solution to exercise 8.1 in the book.

Solution. For the helium ion we have the same wavefunction as for hydrogen atom except Z = 2. This was shown in exercise 6.39.

En = μZ2e4 8ϵ02h2n2n = 1,2

The Bohr radius is:

a0 = ϵ0h2 πμe2

μ in this context is the reduced mass of the nucleus/electron system. The ground state energy is:

E1 = μZ2e4 8ϵ02h2

Thus

E1 = Z2e2 8ϵ0πa0 = Z2e2 2κ0a0

In atomic units e = 1,κ0 = 1,a0 = 1 and for helium Z = 2. Therefore:

E1 = 22 2 = 2a.u.