Find magnetic interaction energy(eV) of electron

[Ed Boon]

Homework Statement

Homework Equations

U=-uz*B=ml*(e*h/2*m)*B
uz=-(2.00232)*(e/2*m)*Sz

The Attempt at a Solution

I thought this was very simple until I re-read it after solving. In the n=1 state for an electron isn't ml equal to 0? so U=0*stuff = 0 but then part b says is there any moment interation for the state so it confused me and now I think I have done it incorrectly. I assume uz is the magnetic moment in terms of Sz but where does the ms=-1/2 come into play? Am I completely going in the wrong direction?
thank you
Ed

 

[anathema]

Dear Ed,

You are correct that in the n=1 state for an electron, the ml quantum number is equal to 0. This means that the orbital angular momentum of the electron is also equal to 0. However, this does not mean that the magnetic moment is equal to 0. The magnetic moment of an electron is determined by its spin, not its orbital angular momentum. The ms quantum number, which represents the spin of the electron, can have two values: +1/2 or -1/2. In this case, we are considering the state with ms=-1/2, which means that the magnetic moment is not equal to 0.

The equation for U that you have provided is correct, but it is missing a factor of -1 for the uz term. The correct equation is U=-uz*B=-(-2.00232)*(e/2*m)*Sz*B. This is the energy associated with the interaction between the magnetic moment (uz) and the external magnetic field (B).

I hope this clarifies things for you. Please let me know if you have any further questions.

 

[baba89]

Hello Ed,

Thank you for your question. The magnetic interaction energy of an electron can be calculated using the following equation:

U = -μ * B = ml * (e * h / 2 * m) * B

Where:
μ = magnetic moment of the electron
B = magnetic field strength
ml = magnetic quantum number
e = elementary charge
h = Planck's constant
m = mass of the electron

To find the magnetic interaction energy in electron-volts (eV), you can use the conversion factor of 1 eV = 1.602 x 10^-19 J.

Now, to address your concerns in the attempt at a solution, the magnetic quantum number (ml) for an electron in the n=1 state can have three possible values: -1, 0, or 1. This means that ml can have a non-zero value, so the magnetic interaction energy would not always be equal to 0. The value of ms = -1/2 is the spin quantum number, which is not directly related to the magnetic interaction energy. It is used to describe the spin of the electron.

I hope this helps clarify your doubts. Let me know if you have any further questions.

Best regards,