522 Atomic PhysicsP42.10Starting with12222m vk eree=we havevk em ree22=and usingrnm k enee=222=givesvk emnm k eneeee22222==ejorvk enne=2=.P42.11Each atom gives up its kinetic energy in emitting a photon,so126 626103 00101 216101 63102348718mvhc==×⋅××=×−−−λ....J sm smJejejejv=×4 42104.m s.P42.12The batch of excited atoms must make these six transitions to get back to state one: 21→, and also32→and 31→, and also 43→and 42→and 41→. Thus, the incoming light must have justenough energy to produce the 14→transition. It must be the third line of the Lyman series in theabsorption spectrum of hydrogen. The absorbing atom changes from energyEi= −= −13 613 6..eV1eV2to Ef= −= −13 60 850..eV4eV2,so the incoming photons have wavelengthλ=−=×⋅×−− −
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