Reading the Spectrum, Ch Atoms in an electric field: the Stark effect and polarizability
Problem
Find the error in the following working for the Stark shift of hydrogen's n=2 level in a field E=1.0×107Vm−1: 'the 2s state has mean radius ⟨r⟩=6a0, so by the sphere model α/4πϵ0=⟨r⟩3=216a03. Using ΔE=−21αE2, this gives a shift of about −9×10−3cm−1, so the whole n=2 level moves down by this small, quadratic amount, just like the ground state but a bit more because the atom is bigger.'
((a)) Carry out this calculation and check the number −9×10−3cm−1 (working in cm−1).
((b)) Identify the physical assumption in the quadratic formula that fails for n=2, and explain why it fails there but not for 1s.
((c)) State the correct type and rough size of the shift, and compare it with the number above.