# Vector model of atom. Hopefully easy question.

1. Sep 7, 2013

### LagrangeEuler

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. Sep 8, 2013

### DrDu

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. Sep 8, 2013

### LagrangeEuler

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