Electron in a one-dimensional box emitting a photon

Click For Summary
SUMMARY

An electron in a one-dimensional box of length 0.300 nm emits a photon when transitioning from energy level E4 to E2. The energy levels are calculated using the formula En = n²E1, where E1 is determined as 4.18 eV. The emitted photon’s wavelength is calculated using λ = hc/(E_i - E_f), resulting in a wavelength of 24.7 nm. The calculations and final result are confirmed as correct by participants in the discussion.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of energy levels in quantum systems
  • Familiarity with the Planck constant (h) and photon energy equations
  • Basic knowledge of wavelength calculations
NEXT STEPS
  • Study the derivation of energy levels in quantum mechanics
  • Learn about the implications of photon emission in quantum systems
  • Explore the relationship between energy and wavelength in electromagnetic radiation
  • Investigate applications of one-dimensional quantum boxes in modern physics
USEFUL FOR

Students of quantum mechanics, physics educators, and anyone interested in the principles of photon emission and energy transitions in quantum systems.

Ezequiel
Messages
18
Reaction score
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 = \frac{h^2}{8mL^2}

λ = \frac{hc}{E_i - E_f}

The Attempt at a Solution



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

So, λ = \frac{hc}{66.9 - 16.7} = 24.7 nm

Is this right?
 
Physics news on Phys.org
Looks good to me. Nice work.
 
Thanks!
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
6K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 2 ·
Replies
2
Views
11K
  • · Replies 3 ·
Replies
3
Views
8K
Replies
1
Views
2K
Replies
4
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K