What Electron Transitions Occur in Helium's Emission Spectrum?

[FsLiu]

Homework Statement

The numbers following are the results of a lab experiment to find the spectral lines of Helium in a gas discharge tube. The lines I got were roughly:

703nm, 660nm, 590nm, 500nm, 490nm, 470nm, 450nm.

The question is, what possible electron transitions could the electrons have went though?

Homework Equations

Energy level of hydrogen like atoms is given by:

E= [(-Z^2)(R)]/n^2

The Attempt at a Solution

I'm getting some crazy answers like transitions from n=20 to n=5, or n=9 to n=5. Intuitively, this does not seem to be correct, although my intuition is based on the hydrogen atom which has visible lines only at n=x to n=2.

So... is this correct?

 

[nate808]

Thank you for your question. The electron transitions in a helium atom can be determined using the Rydberg formula, which is similar to the equation you have provided for hydrogen-like atoms. The Rydberg formula for helium is given by:

1/λ = R (1/4 - 1/n^2)

Where λ is the wavelength of the spectral line, R is the Rydberg constant (1.097x10^7 m^-1), and n is the principal quantum number of the energy level.

Using this formula, we can determine the possible electron transitions for the spectral lines you have observed. Here are a few examples:

- The 703nm line could correspond to a transition from n=4 to n=2 (1/703nm = 1.4x10^7 m^-1 = R(1/4 - 1/4)).
- The 660nm line could correspond to a transition from n=5 to n=2 (1/660nm = 1.5x10^7 m^-1 = R(1/4 - 1/5)).
- The 590nm line could correspond to a transition from n=6 to n=2 (1/590nm = 1.7x10^7 m^-1 = R(1/4 - 1/6)).

As you can see, the electron transitions in helium are not limited to only transitions to the n=2 energy level, like in the hydrogen atom. This is due to the fact that helium has two electrons, which can interact with each other and create more complex energy levels.

I hope this helps to clarify your understanding of the electron transitions in helium. Let me know if you have any further questions.