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 -4.9 eV, -2.9 eV, -2.3 eV, and -2.0 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.)

Smallest energy of a dark line: ??? eV

Next larger energy of a dark line : ??? eV

Next larger energy of a dark line : ??? eV

Explanation / Answer

Absorption happens when an object jumps from one allowed energy state to another allowed energy state.

So the energies it can absorb are the differences between the energies. List all those differences.

For instance 2 eV is an allowed jump, between the -4.9 eV and -2.9 eV energy level and its in the visible light range you were told (1.8 to 3.1 eV).

2.9 eV is another allowed jump, between -4.9 eV and -2 eV. That one is in the visible light range.

2.6 eV is another allowed jump, between -4.9 eV and -2.3 eV. That one is in the visible light range.

0.9 eV is another allowed jump, between -2.9 eV and -2 eV. That one notis in the visible light range.

0.6 eV is another allowed jump, between -2.9 eV and -2.3 eV. That one is not in the visible light range.

2 eV is another allowed jump, between -2.9 eV and -4.9 eV. That one is in the visible light range.

0.3 eV is another allowed jump, between -2.3 eV and -2 eV. That one is not in the visible light range.

0.6 eV is another allowed jump, between -2.3 eV and -2.9 eV. That one is not in the visible light range.

2.6 eV is another allowed jump, between -2.3 eV and -4.9 eV. That one is in the visible light range.

0.3 eV is another allowed jump, between -2 eV and -2.3 eV. That one is not in the visible light range.

0.9 eV is another allowed jump, between -2 eV and -2.9 eV. That one is not in the visible light range.

2.9 eV is another allowed jump, between -2 eV and -4.9 eV. That one is in the visible light range.

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