# Angular momentum and Quantum Number l

• krawls30
In summary, the question discusses two masses connected by a rigid rod rotating about their center of mass with an angular frequency of 800 rad/s. Using the formula for moment of inertia and angular momentum, the value of the quantum number for angular momentum is found to be approximately 1055. However, there may be a mistake in the calculation as the mass of the rod is not taken into account.
krawls30
Move here from another forum, so no homework template.
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 = ∑miri
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!

krawls30 said:
Moment of Intertia about center of mass = ∑miri

Are you sure this is correct?

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

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

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

No you have to square the radius. I = mr^2, not mr.
krawls30 said:
Well I also tried 1/12 ML2 but that still isn't working.
I don;t see that on the page

OH that's my mistake, that was a typo it's supposed to be Σmiri2

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

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

## 1. What is angular momentum in quantum mechanics?

Angular momentum is a physical quantity that describes the rotational motion of a particle. In quantum mechanics, it is represented by the operator L, which is a combination of the position and momentum operators.

## 2. What is the relationship between angular momentum and quantum number l?

The quantum number l represents the magnitude of the angular momentum of a particle. It is related to the orbital angular momentum by the equation L = ħ√(l(l+1)), where ħ is the reduced Planck's constant.

## 3. How does the value of quantum number l affect the energy levels of an atom?

The value of l determines the shape of the electron's orbital, which in turn affects its energy. For example, when l=0, the orbital is spherically symmetric and has the lowest energy level. As l increases, the orbital becomes more complex and the energy level increases.

## 4. What are the possible values of quantum number l?

The quantum number l can have integer values from 0 to n-1, where n is the principal quantum number. This means that for a given energy level, there can be a maximum of n-1 different angular momentum states.

## 5. How does angular momentum affect the behavior of particles in an atom?

Angular momentum plays a crucial role in determining the allowed energy levels and spatial distribution of electrons in an atom. It also affects the magnetic properties of atoms and the interaction between particles in atoms. Additionally, the conservation of angular momentum is a fundamental principle in quantum mechanics.

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