Suppose a collection of quantum harmonic oscillators occupies the lowest 4 energy levels, and the spacing between levels is 0.04 eV. What is the complete emission spectrum for this system? That is, what photon energies will appear in the emissions? Include all energies, whether or not they fall in the visible region of the electromagnetic spectrum. Enter the photon energies in order of increasing energy.

a. Smallest photon energy = ____eV
b. Next larger photon energy = ____eV
c. Largest photon energy = ____eV

Respuesta :

Answer:

a. Smallest photon energy = 0.04 eV

b. Next larger photon energy = 0.08 eV

c. Largest photon energy = 0.12 eV

Explanation:

Since the spacing between the levels is 0.04 even

The smallest photon energy, E= 0.04 eV

The next larger photon energy = 2E = 2×0.04 = 0.08 eV

Largest photon energy = 3E = 3×0.04 = 0.12

The relationships for the atomic transitions allowed to find all the transitions in the four-level system are:

  • The minimum energy is:  E = 0.04 eV.
  • Tthe following is:   E = 0.08 eV.
  • Tthe maximum energy is:  E = 0.12 eV.

Atomic Transitions are the energy deference between two specific atomic levels.

        [tex]\Delta E = E_f - E_i[/tex]  

They indicate that we have 4 equally spaced states with an energy difference of 0.04 eV between each one.

In the attachment we can see a diagram of the system with an arrow indicating the possible transitions.

From level n = 2 to level n = 1 the energy is E₂₁ = 0.04 eV.

from level n = 3 to n = 1 the energy is E₃₁ = 0.08 eV.

all other transitions in the table.

Initial state   final state    Energy (eV)

    4                   1               0.12

    3                   1               0.08

    2                   1               0.04

     

    4                  2              0.08

     3                 2              0.04

   

     4                3               0.04

These are all the possible transitions, we can see that some energies have several possible states, these currents that have several possibilities are called degenerate.

the energies are:

the minimum is:   E = 0.04 eV.

the following is:    E = 0.08 eV.

the maximum  is E: = 0.12 eV.

In conclusion using the relationships for the atomic transitions we can find all the transitions in the four-level system are:

  • The minimum energy is: E = 0.04 eV
  • The following is:  E = 0.08 eV
  • Tthe maximum energy is: E = 0.12 eV

Learn more here:  brainly.com/question/19426165

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