How do we use this to solve for the spacing between levels?

[dscot]

Homework Statement

So I'm stuck on part (ii) where we have to solve the rotational energy levels.

Problem: http://screencast.com/t/9rZStJdG3wJ

The answer is ii) 0, 3.84 cm-1, 11.52 cm-1

Homework Equations

Equations: http://screencast.com/t/ubFEheGBz

The Attempt at a Solution

Calculate the reduced mass then divide by avagardos number and x1000 to get it into kg per molecule - 1.139*10^-26

Then I use this value to work out I and get 1.457*10^-46

Then, B can be calculated I got 603.52 for this

Next, D = 187.7

Put all this into the equation for E and I end up with 460.24 but the actual answer for this case (j=1) was 3.84cm^-1.

Please let me know if there's anything I can clear up.

 

[TSny]

Hello, dscot.

I agree with your value for I. But, I'm getting much smaller values for B and D. Can you show explicitly your calculations?

 

[dscot]

Hi TSny,

Sure no problem :)

B = (6.63*10^-34 / ( 8 * ∏ * 1.457*10^-46 * 3*10⁸
= 603.52

D = 4*(603.52)³ / 2169.7² = 460.24

Thanks!

 

[TSny]

Did you leave out one of the $\pi$'s in the denominator of B?

Think about the units for your answer for B. In the SI system, the unit of length is the meter.

 

[dscot]

Hi,

Sorry I did miss it out when copying it from my notes.

As far as I can tell everything is in meters which I'm now guessing is wrong :)

h, I and C are in meters I think I must be missing something obvious?

Thanks

 

[TSny]

You worked in the SI system, so you're getting B in inverse meters rather than inverse centimeters. That's ok, since you can easily convert from one to the other.

 

[dscot]

Ah, I see so just divide by 100?

When working out D do I just leave We in cm-1 in that case?

Thanks!

 

[TSny]

Yes and Yes

 

[dscot]

Great! Thanks so much TSny :)

I have a similar problem regarding rotational energy levels that seems to be confusing me: Can somebody please tell me what's meant here by calculating the spacing?- a(i) - http://screencast.com/t/BK8BsW7r

We have these formulas available: http://screencast.com/t/ha9UvNfXHG2

I think we may have to use that population given in the question

Nj/Nd = gj exp( -ej/KT ) ?