Parallel vs anti parallel electron spin

[dogeatdog]

Homework Statement

a hydrogen atom with its electron in the ground state 1s orbital can have proton and electron spins that are either parallel or anti parallel. which is the lower configuration and why? treat the electron as orbiting the proton in a plane perpendicular to the spin of the proton.

Homework Equations

the Heitler London model may have something to do with it but I am not sure.
i also know that the splitting of spectral lines is due to the property of spin

The Attempt at a Solution

im pretty sure the answer is anti parallel but i have no idea why. this was assigned for a general physics class which i think is crazy since we never even talked about anything like this. Please Help or steer me in the right direction or something. thanks

 

[nickjer]

I suggest you look up the hyperfine interaction. Hydrogen is a famous case leading to the 21 cm hydrogen line used in radio astronomy.

 

[Cruikshank]

Without calculations, I would answer based on opposite poles of magnets attracting. For a bit more detail, use the energy of a magnetic dipole in a B field.

 

[nickjer]

Without calculations, I would answer based on opposite poles of magnets attracting. For a bit more detail, use the energy of a magnetic dipole in a B field.

The classical solution of magnetic field and dipoles is incorrect in this case. It turns out you have to use quantum mechanics to get the right solution for this problem.

 

[paranormal]

I can provide some explanation for the concept of parallel and anti parallel electron spin in a hydrogen atom. In quantum mechanics, the electron spin is a fundamental property of an electron and it can have two possible orientations, either parallel or anti parallel to the spin of the proton. The ground state of a hydrogen atom has the lowest energy and the electron is found in the 1s orbital. According to the Heitler-London model, the electron in the 1s orbital is in a spherical distribution around the proton, with no preferred direction for its spin.

Now, when we consider the orientation of the electron spin, we need to take into account the effect of the magnetic field created by the spin of the proton. A parallel electron spin means that the electron is spinning in the same direction as the proton, creating a stronger magnetic field and resulting in a higher energy state. On the other hand, an anti parallel electron spin means that the electron is spinning in the opposite direction to the proton, creating a weaker magnetic field and resulting in a lower energy state.

In the case of a hydrogen atom, the electron is orbiting the proton in a plane perpendicular to the proton's spin. This means that the electron can either spin in the same direction as the proton (parallel) or in the opposite direction (anti parallel). Since the anti parallel configuration has a lower energy state, it is the more stable configuration for the hydrogen atom.

The splitting of spectral lines, as you have mentioned, is due to the property of spin. This is known as the Zeeman effect, where the energy levels of an atom are split into sub-levels due to the interaction between the electron spin and the external magnetic field.

I hope this explanation helps you understand the concept of parallel and anti parallel electron spin in a hydrogen atom. The key point to remember is that the anti parallel configuration has a lower energy state, making it the more stable configuration.