With the normal Zeeman effect, I think the splitting of the emission/absorbtion lines is worth [itex]\Delta E = \mu _B B m_l[/itex]. That was before they knew about the spin.(adsbygoogle = window.adsbygoogle || []).push({});

When they discovered the spin they realized that in fact the energy splitting was worth [itex]\Delta E =g_l \mu _B B m_l[/itex] where [itex]g_l=1+\frac{j(j+1)+s(s+1)-l(l+1)}{2j(j+1)}[/itex].

Now for example if I take the hydrogen atom in its ground state, [itex]g_l=2[/itex]. So that the [itex]\Delta E[/itex] is twice as big as what they thought it was before the understanding of the spin.

How could they think that their formula before the spin introduction was "ok"? I mean a factor 2 looks enormous to me. Am I missing something?

Besides, why should one use the formula for the normal Zeeman effect in -undergraduate physics- problems while it doesn't seem (at least to me) give any value close to the real ones? I feel like I'm really missing something.

Can someone shed some light on this?

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# Zeeman effect, something I'm not understanding, about history

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