Basic Quantum Mechanics (Help)

[jjcopl]

Hello, 
I have a difficulty to solve my homework,(I know that I should do it myself, and I am trying), would someone be kind and help me, please?

this is my first homework and it's very important. 

questions 1.3 and 1.4 in the attached file.
Thank you
 

CSiS_Ex1_2018.pdf

[exchemist]

Hello, 

I have a difficulty to solve my homework,(I know that I should do it myself, and I am trying), would someone be kind and help me, please?

this is my first homework and it's very important. 

questions 1.3 and 1.4 in the attached file.

Thank you

 

1.3 does not look not hard. They give you the formula to use and even the numbers to plug in.

 

The only complication I can see is that they give spectral data in wavenumbers (cm-1) rather than frequency. You just need to remember that wavenumber (1/λ) = ν/c, so you multiply wavenumber by c to get a frequency. 

 

Can you work out an answer for the first bit, i.e. for H3+ at 1000K? What do you get? If we can agree on that you should be able to work out the rest, I think.

 

1.4 looks trickier, I must admit. I'll need to think about that one a bit.  

[exchemist]

Further note on 1.4:

 

Difference in energy between successive rotational levels will be E(J+1) - E(J). This will be hcB( (J+1)(J+2) - J(J+1) ) = hcB J²+3J+2 -(J²+J) ) = hcB 2(J+1). This means that the energy gap between successive levels goes up by 2hcB each time, so you get a series of lines in the spectrum that are all 2hcB apart. That's what they mean when they say spacing of the lines in frequency is independent of J.    

 

Does this help get you on the right track? 

 

The rest of the problem seems to lead you through how you can get to a bond length from measuring the rotational spectrum, which is pretty cool! 

Edited April 18, 2018 by exchemist