Angular momentum and Quantum Number l

[krawls30]

The question: Consider two masses of 0.1 gm each, connected by a rigid rod of length 0.5 cm, rotating about their center of mass with an angular frequency of 800 rad/s. a.) What is the value of l corresponding to this situation? b.) What is the energy difference between adjacent l-values for the l you have just calculated?

Relevant equations:
Moment of Intertia about center of mass = ∑m_ir_i
L=I * ω
L= ħ[l(l+1)]^1/2

My attempt at part a of the problem:
r= 0.0025m
mass= 0.0001 kg

I = 2 * (0.0001 kg) * (0.0025 m²) = 1.25 * 10^-9 kg m²

L = 1.25 * 10^-9 kg m² * 800 rad/s

L/ħ = 9.48*10²⁷ = [l(l+1)]^1/2

Which this is the answer, but when I solve for l(the quantum number for angular momentum) I get a number with order of magnitude of 10⁵⁵ am I completely overlooking something here? I can't think of any other ways to solve this problem. Thank you in advance for your help!

 

[barefeet]

Moment of Intertia about center of mass = ∑miri

Are you sure this is correct?

 

[krawls30]

I think so... I used this website http://socratic.org/questions/how-do-you-find-moment-of-inertia-of-two-point-masses

 

[barefeet]

Look again, that gives the another formula than what you wrote

 

[krawls30]

Well I also tried 1/12 ML² but that still isn't working.

 

[barefeet]

No you have to square the radius. I = mr^2, not mr.

Well I also tried 1/12 ML2 but that still isn't working.

I don;t see that on the page

 

[krawls30]

http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html

 

[krawls30]

OH that's my mistake, that was a typo it's supposed to be Σm_ir_i²

 

[barefeet]

If you don't know the mass of the ord you can't use the second equation because M is the mass of the rod

 

[krawls30]

it's a rigid body.. so the mass of the rod is being ignored