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The energy levels of a particular quantum object are −8.2 eV, −4.4 eV, and −1.8 eV. If a collection of these objects is bombarded by an electron beam so that there are some objects in each excited state, what are the energies of the photons that will be emitted?
1. 12.6 eV, 2.6 eV, 10 eV
2. 3.8 eV, 12.6 eV, 2.6 eV
3. −8.2 eV, −4.4 eV, −1.8 eV
4. 3.8 eV, 6.4 eV, 2.6 eV
5. 8.2 eV, −4.4 eV, −1.8 eV
6. −3.8 eV, −6.4 eV, −2.6 eV
7. 6.4 eV, −4.4 eV, 1.8 eV
8. 3.8 eV, 6.2 eV, 12.6 eV
9. 10 eV, −3.8 eV, 6.4 eV
10. 12.6 eV, 10 eV, 6.2 eV

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Answer:

4. 3.8 eV, 6.4 eV, 2.6 eV

Explanation:

Energy levels

[tex]E_1[/tex] = -8.2 ev

[tex]E_2[/tex] = -4.4 ev

[tex]E_1[/tex] = -1.8 ev

The difference in energy levels is given by

[tex]|\Delta E_{12}|=|E_1-E_2|\\\Rightarrow |\Delta E_{12}|=|-8.2-(-4.4)|\\\Rightarrow |\Delta E_{12}|=3.8\ eV[/tex]

[tex]|\Delta E_{13}|=|E_1-E_3|\\\Rightarrow |\Delta E_{13}|=|-8.2-(-1.8)|\\\Rightarrow |\Delta E_{13}|=6.4\ eV[/tex]

[tex]|\Delta E_{23}|=|E_2-E_3|\\\Rightarrow |\Delta E_{23}|=|-4.4-(-1.8)|\\\Rightarrow |\Delta E_{23}|=2.6\ eV[/tex]

Therefore, the energies of the photons that will be emitted are

4. 3.8 eV, 6.4 eV, 2.6 eV

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