Total angular momentum

In summary, the total angular momentum quantum number, J, can be found by considering the different electron configurations and their corresponding angular momenta. For the n=1 state, L=0 and S=0, giving J=0. For the n=2 state, L=0 and S=0, giving J=0. For the n=3 state, L=1 and S=1/2, giving J=7/2. This follows the rule of adding L and S to get the total J. However, only when all the directions of the angular moments are the same can they be added directly. The use of Hund's rule can help clarify this concept.
  • #1
learning_phys
74
0
lets say there is an electron configuraiton of [tex]1s^2 2s^2 2p^2 3p^1[/tex]

I want to find the total angular momentum quantum number, J=L+S

considering the n=1 state, there are two electrons, in the s shell which means one is spin 1/2 and the other is spin -1/2 giving a total spin of 0. The s shell has no angular momentum so L=0.

considering n=2 state, there are two electrons in the s shell which again gives us 0 total angular momentum. If we went to the p shell, there are 2 electrons in the p shell, each having L=1, so we add them together to get L=2. The two electrons do not contribute spin since their net sum is zero, S=1/2-1/2=0.

considering the n=3 state, there is 1 electron in the p shell, which means S=1/2 and L=1

J is the sum of L and S, so the total angular momentum should be J=L+S=2+1+1/2=7/2

Is this correct?
 
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  • #2
anyone?
 
  • #3
help?
 
  • #4
this part of physics is very confused
 
  • #5
vega_1992 said:
this part of physics is very confused

and confused physics confuses me
 
  • #6
only when all the directions of the angular moments be same,can we plus them directly
 
  • #7
Use Hunds rule.
 

1. What is total angular momentum?

Total angular momentum is a physical quantity that describes the rotational motion of a system. It takes into account both the angular momentum of individual objects within the system and the overall rotational motion of the system as a whole.

2. How is total angular momentum calculated?

Total angular momentum is calculated by multiplying the moment of inertia (a measure of an object's resistance to change in rotation) by the angular velocity (the rate at which an object rotates) of the system.

3. What is the conservation of total angular momentum?

The conservation of total angular momentum states that in a closed system, the total angular momentum remains constant. This means that the total angular momentum before and after an interaction or event will be the same.

4. What are the units for total angular momentum?

The units for total angular momentum are kilogram meters squared per second (kg·m^2/s) in the SI system, or pound feet squared per second (lb·ft^2/s) in the imperial system.

5. How does total angular momentum relate to orbital motion?

In orbital motion, the total angular momentum of a system is equal to the product of the mass, orbital radius, and orbital velocity. This relationship is known as Kepler's second law of planetary motion.

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