Spectral lines from multiple atoms

[gildomar]

Homework Statement

"A gas discharge tube contains H 1 , H2, He 3 , He4, Li6, and Li7 ions and atoms (the superscript
is the atomic mass), with the last four ionized so as to have only one electron. (a)
As the potential across the tube is raised from zero, which spectral line should appear
first? (b) Give, in order of increasing frequency, the origin of the lines corresponding to the
first line of the Lyman series of H 1 ."

Homework Equations

The Attempt at a Solution

I have no problem with part (a), but I don't quite get what they're asking for in part (b).

 

[Basic_Physics]

The first line of the Lymann series originates from a transition from the second to the first energy level of hydrogen.
I guess that they want the lines form the other ions and atoms of similar transitions in the order of increasing frequencies. So you need state them in increasing frequencies order and specify from which ion or atom they originate.

 

[gildomar]

That's basically what I was thinking, but the phrase "the origin of" was throwing me off. Without that phrase, that part is also pretty straight-forward, since I would just use the reduced mass Rydberg equation to calculate the frequency of the spectral line in each atom with n: 2->1. But with the phrase, it sounds like they want me to find the frequency for the first Lyman transition for the hydrogen, helium, and lithium without taking the reduced mass effect into account.

 

[mfb]

I think "origin" just means the isotope.

 

[Nickie]

In part (a), the question is asking which spectral line will appear first as the potential across the tube is raised from zero. This is because as the potential increases, the energy of the atoms and ions in the gas discharge tube also increases. As a result, the electrons in these atoms and ions will jump to higher energy levels and then fall back to lower energy levels, emitting photons at specific wavelengths or frequencies. The first spectral line to appear will be the one corresponding to the lowest energy transition, which is typically the transition from the ground state to the first excited state.

In part (b), the question is asking for the origin of the lines corresponding to the first line of the Lyman series of H 1 in order of increasing frequency. The Lyman series is a set of spectral lines that are emitted by hydrogen atoms when an electron transitions from higher energy levels to the ground state. The first line in this series is the Lyman alpha line, which corresponds to the transition from the first excited state (n=2) to the ground state (n=1). The origin of this line is the emission of a photon with a wavelength of 121.6 nm. The next line in the series, Lyman beta, corresponds to the transition from the second excited state (n=3) to the ground state, and has a wavelength of 102.6 nm. This pattern continues for the rest of the Lyman series, with each line corresponding to a different energy transition and emitting photons at shorter and shorter wavelengths.