What Determines the Signs of Magnetic Moments in a Hydrogen Atom?

[alfredbester]

Blard: Consider the hydrogen atom in a magnetic field of 2T. If the atom is its ground state.

(a) Write down the magnetic moments of the proton and the spinning electron.

A: For electron Uz = +/- 0.5gUb = - 9.27E-27 J/T

Since it's the ground state g is 2 (approx)
My question is what should the sign on the value of the mag moment be, my understanding is the first electron position is the upstate.

For proton: Uz = +/- 2.79Un = + 1.41E-26 J/T

Again what should the signs of the mag moment be, I'm assuming it is well defined because it's a hydrogen atom

 

[anathema]

.

Hello Blard,

Thank you for your post regarding the magnetic moments of the hydrogen atom in a magnetic field of 2T. I would like to provide some clarification and additional information.

First, let's define the magnetic moment. It is a measure of the strength and direction of the magnetic field created by a particle, such as an electron or a proton. The magnetic moment is represented by the symbol μ and is measured in units of joules per tesla (J/T).

Now, to answer your first question about the sign of the magnetic moment for the electron in the ground state. The electron has two possible spin states, up or down, which are represented by the symbols +1/2 or -1/2, respectively. In this case, the electron is in its ground state, which means it is in the up spin state. Therefore, the sign of the magnetic moment for the electron would be positive (+0.5gμb) as indicated in your post.

For the proton, it is important to note that the magnetic moment is mainly determined by the spin of the particle, which in the case of a proton is the direction of its intrinsic angular momentum. The proton's spin state is also represented by the symbols +1/2 or -1/2, depending on the direction of its spin. However, unlike the electron, the proton's spin state is not well-defined in a hydrogen atom and can fluctuate. Therefore, the sign of the magnetic moment for the proton would be either positive or negative, depending on its spin state at any given moment.

In conclusion, the signs of the magnetic moments for the electron and proton in a hydrogen atom in a magnetic field of 2T can vary depending on their spin states. I hope this helps clarify your understanding. Thank you for your interest in this topic.

 

[kyle8921]

I would like to clarify that the sign of the magnetic moment for both the proton and electron in the hydrogen atom is dependent on the direction of the magnetic field. If the magnetic field is pointing towards the top of the page, then the magnetic moment of the proton will be pointing up and the magnetic moment of the electron will be pointing down. If the magnetic field is pointing towards the bottom of the page, then the magnetic moment of the proton will be pointing down and the magnetic moment of the electron will be pointing up.

In the ground state of a hydrogen atom, the electron is in the 1s orbital, which has a spherical symmetry. This means that the electron has equal probability of being found in any direction around the nucleus. Therefore, the sign of the magnetic moment of the electron can be either positive or negative, depending on the direction of the magnetic field.

Similarly, the proton also has a magnetic moment, which is dependent on the direction of the magnetic field. In the ground state, the proton's magnetic moment is pointing in the same direction as the electron's magnetic moment, but with a larger magnitude. Again, the sign of the proton's magnetic moment can be either positive or negative, depending on the direction of the magnetic field.

In summary, the signs of the magnetic moments for both the proton and electron in the hydrogen atom are not fixed and can change based on the direction of the magnetic field.