Suppose a hypothetical object has just four quantum states, with the following e

Question

Suppose a hypothetical object has just four quantum states, with the following energies:

-1.0 eV (third excited state)
-1.4 eV (second excited state)
-2.9 eV (first excited state)
-4.9 eV (ground state)

(a) Suppose that material containing many such objects is hit with a beam of energetic electrons that ensures that there are always some objects in all of these states. What are the six energies of photons that could be strongly emitted by the material? (In actual quantum objects there are often "selection rules" that forbid certain emissions even though there is enough energy; assume that there are no such restrictions here.)

List the photon emission energies in order from largest to smallest. If two different transitions would produce photons of the same energy, list that energy twice:

1-   eV (largest)

2-

3-

4-

5-

6-   eV (smallest)

(b) Next, suppose that the beam of electrons is shut off so that all of the objects are in the ground state almost all the time. If electromagnetic radiation with a wide range of energies is passed through the material, what will be the three energies of photons corresponding to missing ("dark") lines in the spectrum? Remember that there is hardly any absorption from excited states, because emission from an excited state happens very quickly, so there is never a significant number of objects in an excited state. Assume that the detector is sensitive to a wide range of photon energies, not just energies in the visible region. List the dark-line energies in order from largest to smallest.
eV (largest)
eV
eV (smallest)

Explanation / Answer

(a)

All you need to do is calculate the difference between each level with all of the other levels. The differences would be

1) ground to first
2) ground to second
3) ground to third
4) first to second
5) first to third
6) second to third

Express the answers as absolute values ( ie positive numbers)

(b)

B. Again, just difference the energies. The available jumps are 1-2, 1-3 and 1-4.

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