Formulas for Angular Momentum An atomic electron's angular momentum, L, is related to its quantum number l by the following equation: L = (h/2p)Ö(l(l+1)) where h is Planck's constant. Since this is quantum mechanics, of course, only certain discrete amounts of angular momentum are allowed; that's why l has to be an integer. The quantum number m refers to the projection of the angular momentum in a direction of your choice, conventionally called the z direction. Lz, the component of angular momentum in the z direction, is given by the formula Lz = m(h/2p) For example, let's say you choose the z direction to be vertical. The pink dotted arrow in this picture represents the vector L. The solid blue and red arrows are its horizontal and vertical components; the length of the vertical red arrow is Lz.

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