By the same construction as

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · Radiative transitions, external fields and collisions

Reading the Spectrum, Ch Atoms in an electric field: the Stark effect and polarizability

Problem

n=2

, the extreme Stark states of the hydrogen

n=3

level (formed from combinations of

3s

3p_0

and

3d_0

) shift by

\pm\tfrac32n(n-1)ea_0E

relative to the field-free level, with

n=3

. Take a field

E = 3.0\times10^{6}\,\mathrm{V\,m^{-1}}

. ((a)) Calculate the shift of the upper extreme state in eV and

\mathrm{cm^{-1}}

. ((b)) Calculate the total splitting (the energy gap between the two extreme states) in

\mathrm{cm^{-1}}

and GHz. ((c)) Calculate the total splitting of the

n=2

level at the same field, and find the ratio of the

n=3

splitting to the

n=2

splitting.

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