Four excited levels of helium lie

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Many-electron atoms and the periodic table

Deriving the Spectrum, Ch Helium: exchange and the variational method

Problem

Four excited levels of helium lie, above the

1^1S

ground state, at

2^3S

19.820\,\mathrm{eV}

2^1S

20.616\,\mathrm{eV}

2^3P

20.964\,\mathrm{eV}

and

2^1P

21.218\,\mathrm{eV}

. Use two rules from the chapter: light cannot change the total spin, and a single photon cannot connect two states that both have zero orbital angular momentum. Take

hc = 1239.84\,\mathrm{eV\,nm}

. ((a)) List the one-photon decays open to

2^1P

and give the wavelength of each. ((b)) Show that neither

2^3S

nor

2^1S

has any allowed one-photon decay, naming the rule that blocks each route. ((c)) A weak line from

2^3P_1

to the ground state is observed. Find its wavelength and say why the chapter's Hamiltonian cannot produce it.

Related theory

Quantum Mechanics

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