Spin & Energy Levels: Can a Proton Have One Energy Level?

[likephysics]

My quantum knowledge is very minimum.
If spin is +/-(1/2), then the proton has 2 energy levels. (for ex: hydrogen)

So, if the spin is just 1/2, there is only one energy level, correct?
Is this possible?

 

[jtbell]

You're referring to two different quantum numbers, which are associated with different aspects of intrinsic angular momentum ("spin").

In general, angular momentum is a vector quantity: it has both magnitude and direction (orientation). The quantum number s is associated with the magnitude of the spin, which is always positive. For a proton (or neutron or electron, for that matter), s = 1/2. The quantum number m_s is associated with the direction (orientation) of the spin. With s = 1/2, we can have either m_s = +1/2 or m_s = -1/2 (often called "spin up" and "spin down"). When a particle is in a magnetic field, its energy depends on the value of m_s.