Question

in zeeman effect what's the "e" stands for? you have not mentioned anywhere for the equation terms.

Answer 1

e very often stands for the electronic charge - the charge on an electron. I don't know, though, if this actually helps with the q. More detail would help ...
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Answer 2

As i remember it, the Zeeman effect is the splitting of orbiting electron energy levels in, say, chromium, in the presence of a magnetic field near the atom. (I think the electric field version is called the Stark effect). It's a small effect (and Nobel prize worthy it seems) compared to other "coupling schemes" in multi electron atoms such as in the transition elements. But in the posted q, I'd guess that the e" referred to electronic charge.-(1.6x10^-19) Coulombs, if i'm right.