system
Given the following post, respond as if you're commenting on Reddit:
human
What happens to the spin of an electron when it leaves a nucleus?

Lets say a photon collides with an atom, causing an electron on the outer shell to be knocked from orbit. 

From a classical sense, I would assume it takes some amount energy to change the spin of a particle, and that this amount of energy would depend on how far it's rotated.  But, if an electron flies off of a nucleus, there could potentially be a magnetic field in ANY direction that the electron will then encounter. This means that  the electrons spin could change to be oriented in any direction after it leaves the nucleus. 

Now, please correct me if I am wrong, but if I am right that changing the spin takes energy based on how much it has been rotated, there is a violation of energy conservation somewhere here, as the photon would contribute a quantized amount of energy that wouldn't be able to account for the future measurement at an arbitrary angle with respect to its original orientation.

Or, am I wrong about energy and if the spin on the electron was originally up, will it just be measured as up in the magnetic field? 


Thanks!
gpt
The spin of an electron is always 1/2, you can never change that. However you can change its projection along some axis. If the Hamiltonian is dependent on some component of the spin vector, then the energy depends on the orientation of the spin of the particle. An example would be an electron in a magnetic field, where the magnetic dipole moment of the electron wants to align with the external magnetic field. You’ll have a splitting of each possible energy energy into a doublet.

I’m not sure what you mean about electrons leaving the nucleus, and magnetic fields pointing in any direction. Can you describe specifically what situation you’re imagining?