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 = 2; nf = 6
Loses: ni = 7; nf = 3
Loses: ni = 6; nf = 3
Loses: ni = 5; nf = 3
Gains: ni = 3; nf = 6

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

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

Explanation / Answer

Energy of the electron in a particular state in H-atom, E = -13.6/n2

Energy gained, E = Ef - Ei = 13.6(1/ni2 - 1/nf2)

Maximum energy is gained for ni = 2 and nf = 6

E2-6 = 13.6(1/22 - 1/62) = 3.02 eV

The shortest wavelength photon will have the maximum energy. So, electron transitioning from state 7 to state 3 will emit the shortest wavelength photon with energy, E = 13.6(1/32 - 1/72) = 1.23 eV

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