Why is the spin of hydrogen atom 1/2 in NMR spectroscopy?

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if the electron has spin 1/2 and proton has spin 1/2, why is the hydrogen atom (which is made of the electron and proton) have spin of 1/2?
 
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It doesn't. Hydrogen can have a spin of either 0 or 1.

Assuming we mean the isotope whose nucleus has one proton and no neutrons.
 
can you add electron and nuclear spin? I thought they were completely different.
 
When we talk about the spin of hydrogen, we are talking about the spin of the hydrogen nucleus (i.e. a proton). The electron doesn't figure into this.
 
Thanks for clarifying everybody.

FYI, when laser cooling is used to make Bose-Einstein condensates with atoms, the electron and nuclear spins both figure into determining whether the atom is a boson or fermion.
 
Ygggdrasil said:
When we talk about the spin of hydrogen, we are talking about the spin of the hydrogen nucleus (i.e. a proton). The electron doesn't figure into this.

you mean the other way around? electron spin matters since it's intrinsic magnetic moment is much greater than the hydrogen nucleus. this is because the proton mass >> electron mass
 
Most of the time I've heard people discuss the spin of hydrogen is in the context of NMR spectroscopy, a technique that measures the energy differences between nuclear spin states in the presence of a magnetic field. For this technique, the spin of the electrons are not important.