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.)

Answer 1

There are six possible energies of photons emitted from an object with four quantum states due to transitions between excited states and the ground state. The photon energies are 3.4 eV, 3.1 eV, 2.1 eV, 0.3 eV, 1.3 eV, and 1.0 eV, corresponding to the differences between the energy levels of transitions.

Step-by-step explanation:

The student is asking about the possible energies of photons that could be strongly emitted by a material whose quantum objects are constantly excited to different energy levels by a beam of energetic electrons. In this particular case, the quantum object has four discrete energy levels: the ground state (-4.7 eV) and three excited states (-2.6 eV, -1.6 eV, and -1.3 eV).

When the object transitions from an excited state to a lower energy state (which may be another excited state or the ground state), a photon is emitted with energy equal to the difference between these two states. Therefore, we can calculate the six possible photon energies by considering all the possible transitions:

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

The energies of the photons are simply the differences in energy between the two states involved in each transition.