# Vector model of atom. Hopefully easy question.

1. ### LagrangeEuler

335
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.

2. ### DrDu

4,088
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.

3. ### LagrangeEuler

335
But if I look this intensity formulas
$$|\vec{l}|+|\vec{s}|\neq |\vec{j}|_{for j=l+s}$$
Right?