Suppose two different hydrogen atoms, labeled A and B, have their electrons in s

Question

Suppose two different hydrogen atoms, labeled A and B, have their electrons in state n = 4. Atom A emits light when its electron transitions directly from the n = 4 state to the n = 2 state. Atom B emits light twice, as its electron first transitions from the n = 4 state to the n = 3 state, then transitions from the n = 3 state to the n = 2 state. (a) Are the three wavelengths of light the same or different? (b) How does the energy of the photon from atom A compare to the total energy of the two photons from atom B?

Explanation / Answer

a) If you look at Balmer series equation, you can see that the transition depends on the difference of inverse square. Thus, three wavelength cannot be same. You can also observe this when you see the hydrogen emission spectrum. b). However, since each quantum energy level can hold given amount of energy, no matter how the energy level goes down, as long as the initial energy level and final energy level is the same, the change in energy is the same. Thus, the total energy emitted should be the same. See balmer series for more.

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