# Homework Help: Angular momentum quantum number and angle

1. Mar 15, 2010

### leviathanX777

1. The problem statement, all variables and given/known data
What are the possible values for the magnetic quantum number ml for an electron whose orbital quantum number is l = 4? What are the allowed values of the angles between L and the zaxis in this case?

2. Relevant equations

3. The attempt at a solution

Is Ml equal to four for the first part? Because the angular momentum quantum number is equal to four?

I have no idea for the second part. I don't have the gradient of the magnetic field of the z-component and don't have any distance or velocity values.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 15, 2010

### gabbagabbahey

How exactly is this equation relevant? The problem is in regard to an electron orbiting a nucleus, not an electron moving through an inhomogeneous magnetic field as in the Stern-Gerlach experiment.

Open your textbook up and read the section on hydrogen like atoms and angular momentum. The allowed values of $m_l$ for any given value of $l$ will be clearly stated in your text.

If $\theta$ is the angle between $\mathbf{L}$ and the z-axis, then $L_z\equiv \mathbf{L}\cdot \textbf{k}=|\mathbf{L}|\cos\theta[/tex]. So, in terms of operators, you would expect $$\hat{L_z}^2=\hat{L}^2\cos^2\hat{\theta}$$ Where the hat is to denote that we are talking about operators here. (i.e. $$\hat{\theta}$$ is an operator whose value upon measurement corresponds to the angle between $\mathbf{L}$ and the z-axis) What are the allowed values when you measure [tex]\hat{L_z}^2$ for an electron in the state $l=4$?

Last edited: Mar 15, 2010