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. ni = 5; nf = 3 A: Loses B: Gains ni = 7; nf = 3 A: Loses B: Gains ni = 5; nf = 7 A: Loses B: Gains ni = 2; nf = 5 A: Loses B: Gains ni = 7; nf = 4 A: Loses B: Gains Tries 0/3 Find the transition where the atom gains the most energy. How much energy does the atom gain? (in eV) A: 1.17 B: 1.46 C: 1.83 D: 2.28 E: 2.86 Tries 0/3 Find the transition which will emit the shortest wavelength photon. What is the energy of the photon of this transition? (in eV) A: 1.09 B: 1.23 C: 1.39 D: 1.58 E: 1.78 PLEASE SHOW WORK

Explanation / Answer

atom will gain energy if n final is greater than n initial, so

initial is 5 final is 3 loses energy

7 3 loses energy

5 7 gains energy

2 5 gains energy

7 4 loses energy

what transition does atom gain most energy? energy gained is

13.6 eV * (1/ni^2 - 1/nf^2) so using this we find 2 to 5 is the greatest gain

with 13.6 * (1/2^2 - 1/5^2) = 2.86 eV

shortest wavelength photon is the transistion that has the greatest energy loss, which is

initial 7 final 3 and energy lost is 13.6 ev*(1/7^2 - 1/3^2) = -1.2336 eV

so energy of photon is 1.23 eV

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