Question

Suppose a hypothetical object has just four quantum states, with the following energies: -1.3 ev (third excited state) -1.6 ev (second excited state) -2.6 ev (first excited state) -4.7 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:

Answer 1

Six different photon energies can be emitted due to transitions between the four quantum states, calculated as the differences in energy between them. These energies are 3.4 eV, 3.1 eV, 2.1 eV, 1.3 eV, 1.0 eV, and 0.3 eV.

Step-by-step explanation:

If a material with objects having four quantum states is hit with electrons, the material can strongly emit six different energies of photons corresponding to the transitions between the excited states and the ground state. The energies of the emitted photons are calculated by finding the difference between the energy levels of the initial and final states.

The six possible transitions and their energy differences (photon energies) in electron volts (eV) from largest to smallest are:

1. From -1.3 eV (third excited state) to -4.7 eV (ground state): 3.4 eV
2. From -1.6 eV (second excited state) to -4.7 eV (ground state): 3.1 eV
3. From -2.6 eV (first excited state) to -4.7 eV (ground state): 2.1 eV
4. From -1.3 eV (third excited state) to -2.6 eV (first excited state): 1.3 eV
5. From -1.6 eV (second excited state) to -2.6 eV (first excited state): 1.0 eV
6. From -1.3 eV (third excited state) to -1.6 eV (second excited state): 0.3 eV

According to the law of conservation of energy, the transition of an electron from an excited state to a lower energy level results in the emission of a photon, the energy of which is equal to the difference in energy between those levels.