# Vector model of atom. Hopefully easy question.

by LagrangeEuler
Tags: atom, model, vector
 P: 250 In system with one electron total angular moment vector ##\vec{j}## is just: $$\vec{j}=\vec{l}+\vec{s}$$ http://selfstudy.in/MscPhysics/BScVectorModelOfAtom.pdf In page 3 author draw a triangle. Intensities of the vectors are ##|\vec{l}|=\sqrt{l(l+1)}\hbar##, ##|\vec{s}|=\sqrt{s(s+1)}\hbar##, ##|\vec{j}|=\sqrt{j(j+1)}\hbar## And then from nowhere ##j=l+s## or ##j=l-s##. Could you please explain me that! Tnx.
 Sci Advisor P: 3,266 These are maximal and minimal possible values, respectively. If you add two vectors, the length of the sum will always lie between these two extremal values.
 P: 250 But if I look this intensity formulas $$|\vec{l}|+|\vec{s}|\neq |\vec{j}|_{for j=l+s}$$ Right?

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