Suppose you had a collection of a large number of hypothetical quantum objects,

Question

Suppose you had a collection of a large number of hypothetical quantum objects, each of whose individual energy levels were -4.5 eV, -2.9 eV, -2.1 eV, and -1.5 eV. If nearly all of these identical objects were in the ground state, what would be the energies of dark spectral lines in an absorption spectrum if visible white light (1.8 to 3.1 eV) passes through the material? Enter the energies in order of increasing energy, followed by entering 0 in any later boxes for which there is no dark line within the visible spectrum. (That is, if your answers were 1, 2, and 3 eV, you would enter 1 in the first box, 2 in the second box, and 3 in the third box. If your answers were 1 and 2 eV, you would enter 1 in the first box, 2 in the second box, and 0 in the third box. If your answer is just 1 eV, you would enter 1 in the first box, 0 in the second box, and 0 in the third box.)

Explanation / Answer

The ground state is -4.5 eV.

A particle in this state can absorb 2.4 eV to get to -2.1 eV, and 3 eV to get to -1.5 eV.

Next consider a particle that got to -2.1 eV. This particle cannot absorb any of the given energies to get to an allowed energy level. The same goes for the particle that gets to -1.5 eV.

Hence the answer is 2.4, 3, 0.

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