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

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The discussion clarifies that a proton, possessing a spin quantum number (s) of 1/2, can exhibit two distinct energy levels due to its magnetic spin orientations, represented by the magnetic quantum number (m_s) values of +1/2 and -1/2. This results in the proton having two energy states, commonly referred to as "spin up" and "spin down." The relationship between spin and energy levels is crucial in quantum mechanics, particularly when considering particles in magnetic fields.

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

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