Solving Quantum Objects: A Guide to Energy-Level Diagrams

[lebprince]

Homework Statement

Suppose we have reason to suspect that a certain quantum object has only three quantum states. When we excite a collection of such objects we observe that they emit electromagnetic radiation of three different energies: 0.8 eV (infrared), 2.1 eV (visible), and 2.9 eV (visible).
(a) Draw a possible energy-level diagram for one of the quantum objects, which has three bound states. On the diagram, indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. When you are sure that your energy-level diagram is consistent with the observed photon energies, enter the energies of each level (K+U, which is negative). Enter ALL levels before submitting; all of the energies must be correct to be properly scored. The energy K+U of the ground state is -6 eV.

Find energy of highest level (2nd excited state)
Find energy of next highest level (1st excited state)

i have no idea how to approach this problem...any help will be appriciated

 

[lebprince]

i solved it thanks

 

[thomate1]

I would approach this problem by first understanding the basic principles of quantum mechanics and energy-level diagrams. I would then use this knowledge to analyze the given information and draw a possible energy-level diagram for the quantum object in question.

To find the energy of the highest level (2nd excited state), I would use the formula E=K+U, where E is the total energy, K is the kinetic energy, and U is the potential energy. The ground state has an energy of -6 eV, so the 2nd excited state would have an energy of -6 eV + 2.9 eV = -3.1 eV.

Similarly, to find the energy of the next highest level (1st excited state), I would use the formula E=K+U. The 1st excited state would have an energy of -6 eV + 2.1 eV = -3.9 eV.

After finding the energies of each level, I would check if they are consistent with the observed photon energies of 0.8 eV, 2.1 eV, and 2.9 eV. If they match, then my energy-level diagram is consistent with the observations. If they do not match, I would need to revise my diagram and continue to make adjustments until it accurately represents the observed photon energies.

In conclusion, solving quantum objects and creating energy-level diagrams requires a strong understanding of quantum mechanics and the ability to analyze and interpret data. By following the principles and formulas of quantum mechanics, a scientist can accurately depict the energy states of a quantum object and explain the observed phenomena.