Spectral lines from electron energy transitions in this atom

[Jeff97]

Homework Statement

1. On the above diagram draw the other spectral lines in their correct relative positions. Label all
the lines using the letters that are given.
2. Use the letter ‘R’ to label the line at the red end of the spectrum. Give a reason for you answer.

Relevant Equations

See the diagram below.

Do they mean something like this?

 

[mfb]

Do they mean something like this?

Yes, the diagram will look a bit like this, but with a much smaller number of lines.

How is the frequency of a transition related to the energy levels? You can draw the diagram based on that.

 

[collinsmark]

Homework Statement:: 1. On the above diagram draw the other spectral lines in their correct relative positions. Label all
the lines using the letters that are given.
2. Use the letter ‘R’ to label the line at the red end of the spectrum. Give a reason for you answer.
Relevant Equations:: See the diagram below.

View attachment 259606
Do they mean something like this?
View attachment 259607

'Something like that but with far fewer lines.

From the way I understand the problem,
o There are only 4 lines total that you need to draw.
o One of the lines is already drawn for you (although it's not labeled yet).
o Each line that you need to draw will correspond with one of the existing tic marks (not all tic marks will have a line).
o You need to properly label each line (a, b, c, or d). In addition, label one of the lines as "R" indicating the "red" end of the spectrum (and give a reason).

 

[Jeff97]

Yes, the diagram will look a bit like this, but with a much smaller number of lines.

How is the frequency of a transition related to the energy levels? You can draw the diagram based on that.

The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. The higher the frequency, the shorter the wavelength.

Now, @collinsmark I was thinking The first line already plotted is most likely a Paschen series line going from n=4 to n=3 meaning it is line a? If I was to follow on doing this line b would be a Balmer series, line c would be Lyman series so would line d ? From this, I gather R is a. Why because Longer wavelengths will have lower frequencies, and shorter wavelengths will have higher frequencies red is a big wavelength i.e a low frequency. Would the plotting would look something like this ?:

a is already plotted, b at 3rd tic, c at 6th tic, d at 8 or 9?

 

[SammyS]

... Would the plotting would look something like this ?:

a is already plotted, b at 3rd tic, c at 6th tic, d at 8 or 9?

I agree with all but d.

How does the energy (difference) of d compare to the energy (difference) of a and the energy (difference) of c .

 

[Jeff97]

I agree with all but d.

How does the energy (difference) of d compare to the energy (difference) of a and the energy (difference) of c .

d is n=4 to n=1 so it's Lyman are you saying it's tic 7?

 

[collinsmark]

Don't worry about Paschen series, Balmer series, or Lyman series. What you are being asked to show is hypothetical and doesn't belong to any series in particular.

a is already plotted, b at 3rd tic, c at 6th tic, d at 8 or 9?

Looking at the state transition diagram, what is the energy difference between \mathrm{c} and \mathrm{d} (in terms of energy)? More specifically, ask yourself what is that energy difference of that, specifically in terms of the energy of \mathrm{a}?

Now ask yourself, what is the difference in frequency difference between \mathrm{c} and \mathrm{d} in terms of the frequency of \mathrm{a}?

 

[Merlin3189]

I think you need to look at two things:
What is the "relevant equation" ?
What is the ratio of the energies of a) the levels, then from that, b) the transitions ?

Edit: Bold ratio

 

[SammyS]

I agree with all but d.

How does the energy (difference) of d compare to the energy (difference) of a and the energy (difference) of c .

Let me clarify.
In post #5, when I said I agreed with all but d, I was was only referring to the portion of your post that was quoted. In other words, I was only referring to your proposed placement of the spectral lines on the graph.

I was not referring to your labeling of series as Balmer, Lyman, etc. As @collinsmark said, forget those labels. They have no place here.

 

[Jeff97]

Line a frequency is based on n=4 to n=3, frequency= 1.599x10^14 Hz energy= 1.1x10^-19J
Line b based on n=4 to n=2 frequency =6.168x10^14Hz energy=4.1x10^-19J
Line c based on n=3 to n=1 frequency= 2.924x10^15Hz energy =1.9x10^-18J
Line d based on n=4 to n=1 frequency= 3.084x10^15Hz energy = 2x10^-18J

So based on this I gather a is already plotted and can be labelled R, b can be plotted on the third tic, c can be plotted at the 6th and d is almost directly on by it

 

[SammyS]

Line a frequency is based on n=4 to n=3, frequency= 1.599x10^14 Hz energy= 1.1x10^-19J
Line b based on n=4 to n=2 frequency =6.168x10^14Hz energy=4.1x10^-19J
Line c based on n=3 to n=1 frequency= 2.924x10^15Hz energy =1.9x10^-18J
Line d based on n=4 to n=1 frequency= 3.084x10^15Hz energy = 2x10^-18J

So based on this I gather a is already plotted and can be labelled R, b can be plotted on the third tic, c can be plotted at the 6th and d is almost directly on by it

Where did you get these values for the frequencies?

This is just a hypothetical problem.

You are given a diagram with four energy levels, and four possible transitions. The (vertical) spacing of the energy levels is to scale. It looks like you have labeled them from 1 to 4, starting at the bottom. That's good. It makes the discussion easier.

The distance from level 3 to 4 is the least. The distance from level 2 to 3 looks to be twice the distance from 3 to 4. Then finally, the distance from level 1 to 2 looks to be twice the distance from 2 to 3.

So, if you say that energy difference from level 3 to level 4 is 1.1 × 10 ⁻¹⁹ J, then it's twice that from 2 to 3 and 4 times that from 1 to 2.

 

[Jeff97]

So in conclusion, a is already plotted, b at 3rd tic, c at 6th tic, d at 7th tic. And I'm labelling a R as Longer wavelengths will have lower frequencies, and shorter wavelengths will have higher frequencies, red is a big wavelength i.e a low frequency.

https://www.physicsforums.com/conversations/my-question.196887/reply?quote=288074 https://www.physicsforums.com/conversations/my-question.196887/reply?quote=288074
https://www.physicsforums.com/conversations/messages/288074/report

 

[SammyS]

So in conclusion, a is already plotted, b at 3rd tic, c at 6th tic, d at 7th tic. And I'm labeling a R as Longer wavelengths will have lower frequencies, and shorter wavelengths will have higher frequencies, red is a big wavelength i.e a low frequency.

https://www.physicsforums.com/conversations/my-question.196887/reply?quote=288074 https://www.physicsforums.com/conversations/my-question.196887/reply?quote=288074
https://www.physicsforums.com/conversations/messages/288074/report

Yes. That's all correct !