Five possible transitions for a hydrogen atom are listed below: Select whether t

Question

Five possible transitions for a hydrogen atom are listed below: Select whether the atom gains or loses energy for each transition.

Gains: ni = 4; nf = 7
Gains: ni = 3; nf = 4
Gains: ni = 2; nf = 5
Loses: ni = 7; nf = 3
Loses: ni = 4; nf = 2

Find the transition where the atom gains the most energy. How much energy does the atom gain?
2.86 eV

Find the transition which will emit the shortest wavelength photon. What is the energy of the photon of this transition?



I just need help with the last question, it's driving me crazy.

Explanation / Answer

) The atom gains energy if nf > ni

"i" signifies "initial" and "f" signified "final".

2) For a hydrogenic one-electron aton, the atom gains the most energy when
1/ni^2 - 1/nf^2 is largest.

3) To emit a photon, the atom must lose energy. For the shortest wavelength,
1/ni^2 -1/nf^2 is the most negative.

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