Vector model of atom. Hopefully easy question.

In summary, the conversation discusses the total angular momentum vector in a system with one electron, which is denoted by the symbol ##\vec{j}##. The author draws a triangle on page 3 of the provided resource, representing the intensities of the three vectors involved: ##\vec{l}##, ##\vec{s}##, and ##\vec{j}##. The intensities are calculated using the formulas ##|\vec{l}|=\sqrt{l(l+1)}\hbar##, ##|\vec{s}|=\sqrt{s(s+1)}\hbar##, and ##|\vec{j}|=\sqrt{j(j+1)}\hbar##. The conversation then mentions that the maximal and minimal values for
  • #1
LagrangeEuler
717
20
In system with one electron total angular moment vector ##\vec{j}## is just:
[tex]\vec{j}=\vec{l}+\vec{s}[/tex]
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.
 
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  • #2
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
But if I look this intensity formulas
[tex]|\vec{l}|+|\vec{s}|\neq |\vec{j}|_{for j=l+s}[/tex]
Right?
 

1. What is the vector model of an atom?

The vector model of an atom is a representation of an atom that shows the arrangement of electrons around the nucleus. It is based on the idea that electrons move in specific orbits around the nucleus, similar to the way planets orbit around the sun.

2. Who proposed the vector model of an atom?

The vector model of an atom was first proposed by Niels Bohr in 1913. It was later expanded upon by Arnold Sommerfeld in 1916.

3. How does the vector model explain the stability of atoms?

The vector model explains the stability of atoms by showing that electrons are restricted to specific orbits around the nucleus. These orbits, or energy levels, have fixed energy values and do not allow electrons to spiral into the nucleus. This allows atoms to remain stable and not collapse.

4. What is the significance of the vector model in understanding atomic structure?

The vector model was a significant development in understanding atomic structure because it provided a visual representation of the arrangement of electrons in an atom. It also helped explain the spectral lines observed in atoms and led to the development of quantum mechanics.

5. How does the vector model differ from the modern quantum mechanical model?

The vector model differs from the modern quantum mechanical model in that it only works for simple atoms with one electron, while the quantum mechanical model can be applied to all atoms. The quantum mechanical model also takes into account the wave-like nature of electrons, while the vector model treats them as particles. Additionally, the quantum mechanical model does not have fixed orbits for electrons, but rather probability clouds where electrons are likely to be found.

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