What Is the Shortest Wavelength Photon an Electron Can Emit in a Quantum Trap?

[hvthvt]

Homework Statement

There is a thin tube in which a finite potential trap has been set up where V2 = 0 V. An electron is shown traveling rightward toward the trap, in a region with a voltage of V1 = -9.00 V, where it has a kinetic energy of 2.00 eV. When the electron enters the trap region, it can become trapped if it gets rid of enough energy by emitting a photon. The energy levels of the electron within
the trap are E1 = 1.0, E2 = 2.0, and E3 = 4.0 eV, and the nonquantized region begins at E4 = 9.0 eV as shown in the energy-level diagram of Figure b. What is the shortest wavelength such a photon can have?

Homework Equations

E= hc/λ
Ekin=1/2mv²

The Attempt at a Solution

I guess the shortest wavelength occurs at the highest energy level, that is, in the nonquantinized region? However, I do not know what to do with the given voltages. I know that E=qV
Can somebody help me?

 

[Redbelly98]

The Attempt at a Solution

I guess the shortest wavelength occurs at the highest energy level, that is, in the nonquantinized region? However, I do not know what to do with the given voltages. I know that E=qV
Can somebody help me?

Photons (and wavelengths) do not occur at a single energy level, they occur when the electron makes a transition between two different energy levels.

So, to modify your statement, the shortest wavelength occurs when the energy difference between two levels is highest.

You need to figure out the energy difference between the electron's initial state and the possible final states, and use that to figure out the wavelength.

A good starting point is to figure out the initial energy of the electron, using the information given in the problem statement.