Spectral lines in the emission spectrum for an electron at n= 3

[Pushoam]

Homework Statement:

Find the spectral lines of in the emission spectrum for an electron excited to 3rd Orbit.

Relevant Equations:

One line belonging to n=3 to n =1or two lines belonging to n=3 to n =2 and then n=2 to =1.

Since there is only one excited electron, it could come from n=3 to n =1directly or n=3 to n =2 and then n=2 to =1.

Hence, there could be one or two lines depending upon the path taken by electron.
Is this right?

 

[TSny]

Yes. This assumes you're considering a simplified model of hydrogen, say, where effects due to electron spin are ignored. In particular, the assumption here is that there is only one energy value corresponding to a particular value of n.

Instead of saying there could be one or two lines depending upon the path taken by the electron, I think most people would say there are three lines that can be produced corresponding to the initial state n = 3. This is because emission spectra are usually generated by repeated transitions from many atoms. Some of these transitions are directly from $3 \rightarrow 1$ and some are the indirect $3 \rightarrow 2 \rightarrow 1$. So, all three lines would occur in the spectrum. But you are thinking about it correctly.

 

[Pushoam]

Thank you.