Quantum mechanics , total orbital angular momentum?

[Outrageous]

Homework Statement

A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l?

Homework Equations

n>l, l is bigger or equal to m

The Attempt at a Solution

The allowed l= 3,2,1
The allowed m for largest l= 3,2,1,0,-1,-2,-3
Total orbital angular momentum is the sum of all Lz or L^2?
Ans, total= 3+2+1+0 +(-1)+(-2)+(-3)=0?
L^2= 3(3+1)hbar
What is the total orbital angular momentum?
Please guide ,thanks

 

[vela]

Homework Statement

A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l?

Homework Equations

n>l, l is bigger or equal to m

The Attempt at a Solution

The allowed l= 3,2,1
The allowed m for largest l= 3,2,1,0,-1,-2,-3
Total orbital angular momentum is the sum of all Lz or L^2?
Ans, total= 3+2+1+0 +(-1)+(-2)+(-3)=0?
L^2= 3(3+1)hbar
What is the total orbital angular momentum?
Please guide ,thanks

Read your textbook and notes and answer the following questions:

1. What does ##\vec{L}^2## physically represent?
2. What about ##L_z##?
3. How are ##l## and ##m## related to ##\vec{L}^2## and ##L_z##?

 

[Outrageous]

Read your textbook and notes and answer the following questions:

1. What does ##\vec{L}^2## physically represent?
2. What about ##L_z##?
3. How are ##l## and ##m## related to ##\vec{L}^2## and ##L_z##?

##\vec{L}^2## mean the angular momentum square
##L_z## angular momentum in z direction
##\vec{L}^2##=l(l+1)\hbar and ##L_z##=m\hbar.
Total orbit angular momentum is j?
J=l-(1/2) or l+(1/2)

 

[vela]

##\vec{L}^2## mean the angular momentum square
##L_z## angular momentum in z direction
##\vec{L}^2=l(l+1)\hbar## and ##L_z=m\hbar##.

That should be ##\vec{L}^2=l(l+1)\hbar^2##. Total orbital angular momentum means not just the z-component. ##m## and ##l## are quantum numbers, not angular momenta.

Total orbit angular momentum is j?
J=l-(1/2) or l+(1/2)

The key word here is orbital. Which observable corresponds to orbital angular momentum?

 

[HalfLostAndSearching]

I would first clarify the question to ensure I understand it correctly. It seems that the question is asking for the magnitude of the total orbital angular momentum for a hydrogen atom with a principal quantum number (n) of 4 and the largest possible value of the angular momentum quantum number (l).

In this case, the allowed values of l are 3, 2, and 1, as you correctly stated. However, the allowed values of m depend on the value of l. For l=3, the allowed values of m are -3, -2, -1, 0, 1, 2, and 3. So the total orbital angular momentum would be the sum of the angular momentum for each allowed value of m, which is 0 in this case.

The formula for the total orbital angular momentum is L = √(l(l+1))ħ. Plugging in the largest allowed value of l, which is 3, we get L = √(3(3+1))ħ = √12ħ = 2√3ħ. Therefore, the magnitude of the total orbital angular momentum for a hydrogen atom in the state with n=4 and the largest allowed value of l is 2√3ħ.