Physics 2000 Science Trek Elements as Atoms

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)(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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