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Homework Help: Angular momentum quantum number and angle

  1. Mar 15, 2010 #1
    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

    2.php?z=100&eq=tan\alpha%20%3D%20\frac{d}{m%20v^2}\mu_z%20\frac{\partial%20B_z}{\partial%20z}%20.jpg


    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. jcsd
  3. Mar 15, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    How exactly is this equation relevant?:confused: 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 [itex]m_l[/itex] for any given value of [itex]l[/itex] will be clearly stated in your text.


    If [itex]\theta[/itex] is the angle between [itex]\mathbf{L}[/itex] and the z-axis, then [itex]L_z\equiv \mathbf{L}\cdot \textbf{k}=|\mathbf{L}|\cos\theta[/tex]. So, in terms of operators, you would expect

    [tex]\hat{L_z}^2=\hat{L}^2\cos^2\hat{\theta}[/tex]

    Where the hat is to denote that we are talking about operators here. (i.e. [tex]\hat{\theta}[/tex] is an operator whose value upon measurement corresponds to the angle between [itex]\mathbf{L}[/itex] and the z-axis)

    What are the allowed values when you measure [tex]\hat{L_z}^2[/itex] for an electron in the state [itex]l=4[/itex]?
     
    Last edited: Mar 15, 2010
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