Show, using directional arrows, which transition corresponds to

[IntegrateMe]

Show, using directional arrows, which transition corresponds to...

An energy level diagram is provided. Show, using directional arrows, which transition corresponds to the yellow light and which transition corresponds to the blue light.

http://i.imgur.com/Dv670.jpg?1

I'm not really sure how I'm to go about doing this. How do I know which energy transition corresponds to yellow light and which energy transition corresponds to blue light? Like, 3 to 1 corresponds to yellow and 2 to 1 corresponds to blue?

Please help!

 

[berkeman]

An energy level diagram is provided. Show, using directional arrows, which transition corresponds to the yellow light and which transition corresponds to the blue light.

http://i.imgur.com/Dv670.jpg?1

I'm not really sure how I'm to go about doing this. How do I know which energy transition corresponds to yellow light and which energy transition corresponds to blue light? Like, 3 to 1 corresponds to yellow and 2 to 1 corresponds to blue?

Please help!

Which photon has more energy? A blue one or a yellow one? Do you know the equation that relates the photon's energy to its wavelength?

 

[IntegrateMe]

Yes, I know blue light has more energy than yellow light. Does that mean that for blue light, the arrow would be drawn from 3 to 1, and for yellow light from 2 to 1?

 

[berkeman]

Yes, I know blue light has more energy than yellow light. Does that mean that for blue light, the arrow would be drawn from 3 to 1, and for yellow light from 2 to 1?

I believe that is correct. You should check to see what the ratio of the wavelengths is for blue versus yellow light, to see if that matches the ratio of those two transitions. It's possible that the yellow light might be a 3-->2 transition, but you should be able to figure that out from the ratio of the wavelengths.

 

[IntegrateMe]

Thank you!

 

[IntegrateMe]

Sorry, let's say the wavelengths of the yellow and blue lights, respectively, are:

610 nm and 390 nm

How would I determine where the arrows are drawn using the ratio of these numbers?

 

[berkeman]

Sorry, let's say the wavelengths of the yellow and blue lights, respectively, are:

610 nm and 390 nm

How would I determine where the arrows are drawn using the ratio of these numbers?

The energy is proportional to frequency, right? So the ratio of the frequencies (or the inverse of the ratio of the wavelengths) should equal the ratio of the two arrows you draw for the transitions that generate these photons...

EDIT -- "equal the ratio of the lengths of the two arrows..."

 

[IntegrateMe]

So the blue arrow should be 1.5 times the length of the yellow arrow? So I would draw blue from 3 to 1 and yellow from 1.5 to 1?

 

[berkeman]

So the blue arrow should be 1.5 times the length of the yellow arrow? So I would draw blue from 3 to 1 and yellow from 1.5 to 1?

The energy transitions need to start and end on those lines, so I'm guessing 3-->1 and 2-->1. They may not have been as careful as they should have been in drawing the diagram to scale. Your two choices for the yellow photon transition would be 3-->2 or 2-->1. Which one comes closer to giving you the right ratio? Also, double check the values for the wavelengths of the two colors just to be sure.

 

[IntegrateMe]

This is a 3 part problem, and I pulled the wavelengths directly from the printed text on the page. Just double checked and their right.

Well, if the energy ratio is ~1.6:1, that means the blue arrow should be ~0.6*yellow arrow. So that small gap is supposed to represent the 0.6, which means we should draw blue from 3 to 1 and yellow from 2 to 1?

 

[berkeman]

This is a 3 part problem, and I pulled the wavelengths directly from the printed text on the page. Just double checked and their right.

Well, if the energy ratio is ~1.6:1, that means the blue arrow should be ~0.6*yellow arrow. So that small gap is supposed to represent the 0.6, which means we should draw blue from 3 to 1 and yellow from 2 to 1?

Yes, I believe so -- that is the best fit to the figure.

 

[IntegrateMe]

Thank you again!