Determine electronic transitions by the emitted wavelength?

Click For Summary
SUMMARY

The electronic transition of He II that emits a photon at 468.6 nm corresponds to the Pashen-alpha line. This transition can be analyzed using the equation \(\frac{1}{\lambda}=4R\left(\frac{1}{m^2}-\frac{1}{n^2}\right)\), where \(R\) is the Rydberg constant, \(m\) is the final energy level, and \(n\) is the initial energy level. The energy levels of He II, which is a once-ionized helium atom, can be modeled using the Bohr model with \(Z=2\). The values of \(n\) and \(m\) can be determined through trial and error, as they must be integer values close to the calculated wavelength.

PREREQUISITES
  • Understanding of the Bohr model of the hydrogen atom
  • Familiarity with the Rydberg formula for spectral lines
  • Knowledge of electronic transitions in atomic physics
  • Basic algebra for solving equations with two unknowns
NEXT STEPS
  • Study the Rydberg formula in detail for various elements
  • Learn about the differences between He I and He II in terms of electronic structure
  • Explore the concept of spectral lines and their significance in quantum mechanics
  • Investigate the application of the Bohr model to multi-electron systems
USEFUL FOR

Students of atomic physics, educators teaching quantum mechanics, and anyone interested in understanding electronic transitions in helium and other elements.

FountainPen
Messages
2
Reaction score
0

Homework Statement


What is the electronic transition of He II when it emits 468.6 nm photon.

Homework Equations


\frac{1}{\lambda}=4R\left(\frac{1}{m^2}-\frac{1}{n^2}\right)

The Attempt at a Solution


I know it is a pashen-alpha line from googling but I don't know how to find that from this equation with two unknowns. I know the energy levels are discrete so there is probably only one transition that makes this wavelength. Don't know why He II and not He I so I might be missing something.
 
Physics news on Phys.org
HeI is the neutral He atom, HeII is the once-ionized helium, it has a single electron. The energy levels of HeII can be treated with the Bohr model, with Z=2.

You can find n and m by trial and error. They must be integer numbers in principle. m is the final state, it can be 1, 2, 3,... Find n for each of them. Because of the uncertainty of the wavelength, it will not be an integer number exactly, but it has to be very close to an integer.

ehild
 
Thanks for explaining what He II is. I thought there would be some sort of mathematical way to determine the transition without brute force. Oh well.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 11 ·
Replies
11
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 7 ·
Replies
7
Views
1K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
857
  • · Replies 11 ·
Replies
11
Views
3K
Replies
2
Views
2K