Electron in a one-dimensional box emitting a photon

In summary, an electron in a one-dimensional box can emit a photon when it drops from a higher energy level to a lower one. This is a fundamental concept in quantum mechanics and is demonstrated in a one-dimensional box to show the principles of quantization and quantized energy levels. The energy of the emitted photon is directly related to the energy difference between the two energy levels of the electron, and multiple photons can be emitted if the electron drops multiple times.
  • #1
Ezequiel
19
0

Homework Statement



An electron in a one-dimensional box emits a photon when it moves from energy level E4 to E2. Find the wavelength of the emitted photon.

Length of the box L = 0.300 nm

Homework Equations



En = n2E1
E1 = [itex]\frac{h^2}{8mL^2}[/itex]

λ = [itex]\frac{hc}{E_i - E_f}[/itex]

The Attempt at a Solution



E1 = 4.18 eV
E2 = 22 E1 = 16.7 eV
E4 = 42 E1 = 66.9 eV

So, λ = [itex]\frac{hc}{66.9 - 16.7}[/itex] = 24.7 nm

Is this right?
 
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  • #2
Looks good to me. Nice work.
 
  • #3
Thanks!
 

FAQ: Electron in a one-dimensional box emitting a photon

1. What is an electron in a one-dimensional box emitting a photon?

An electron in a one-dimensional box emitting a photon refers to the phenomenon where an electron, confined to a one-dimensional space, releases a photon of electromagnetic radiation. This is a fundamental concept in quantum mechanics.

2. How does an electron emit a photon in a one-dimensional box?

In a one-dimensional box, an electron can only occupy certain energy levels. When an electron drops from a higher energy level to a lower one, it releases energy in the form of a photon. This process is known as emission.

3. What is the significance of a one-dimensional box in this scenario?

A one-dimensional box represents a simplified model of a confined space. It is used to demonstrate the quantum mechanical principles of quantization and quantized energy levels.

4. What is the relationship between the energy of the emitted photon and the energy levels of the electron?

The energy of the emitted photon is directly related to the energy difference between the two energy levels of the electron. This is known as the energy conservation principle.

5. Can an electron in a one-dimensional box emit multiple photons?

Yes, an electron in a one-dimensional box can emit multiple photons if it drops from higher energy levels to lower ones multiple times. Each emission would result in a photon with a specific energy and wavelength.

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