Question

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

Loses Gains  n_i = 7; n_f = 4
Loses Gains  n_i = 4; n_f = 6
Loses Gains  n_i = 2; n_f = 6
Loses Gains  n_i = 7; n_f = 3
Loses Gains  n_i = 3; n_f = 5

Tries 0/10

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

Tries 0/10

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

Answer 1

When electron gains energy, it excited from lower energy level to higher energy level, when it lose energy electron deexcited to lower level.

ni = 7; nf = 4 ;   energy  Loses

ni = 4; nf = 6; energy gains

ni = 2; nf = 6    energy gains

ni = 7; nf = 3   energy  Loses

ni = 3; nf = 5   energy gains

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Atom gains more energy when  ni = 2; nf = 6.

The energy of electron in Hydrogen atom in nth level

En = - 13.6 / n²

For 2nd level:   E2 = - 13.6 / 2² = -3.4 eV

For 6th level:   E6 = - 13.6 / 6² = -0.378 eV

Gain energy = -3.4 - ( -0.378 ) = - 3.02 eV

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Shortest wavelength corresponds to highest energy ( when  ni = 2; nf = 6. )

E = h c / λ

Rearrange for λ

λ = hc / E = 1240 ev.nm / 3.02 eV = 411 nm