Can hydrogen atoms with same electron spin combine?

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MrBrown90
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Paulis exclusion principle say that two electrons around a nucleus can't have the same quantum number. Does that mean that, say, two hydrogen atoms with electrons with the same spin can't make hydrogen gas? Or does one of the electrons change its spin?
 
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In deed spin polarized hydrogen atoms have a very small probability to recombine (which is only possible due to the very weak spin spin interactions between electron and nuclear spin).