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In the 1996 gre exam this scenario comes up in a question: a beam of neutral hydrogen atoms in their ground state pass through a region of of strong inhomogenous magnetic field. In the official answer the answer is that it gets deflected into two beams. I am skeptical of this because the question explicitly states that atoms are in their ground state which would imply that they are in a singlet state and hence behave as spin 0 particles. Why would this not be the case?

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The hydrogen atom has a single electron with spin $S=1/2$. Spin multiplicity can be understood as $2S+1$, or in the case of electrons, the number of unpaired electron plus one. The ground state of the hydrogen atom is not singlet, but doublet, hence the splitting into two parts.

Please note that a system being in ground state does not imply a singlet spin multiplicity.

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