Question

calculate possible angles between L vector and s vector for f electron​

Answer 1

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• In physics, in particular quantum mechanics, the vector model of the atom is a model of the atom in terms of angular momentum.It can be considered as the extension of the Rutherford-Bohr-Sommerfeld atom model to multi-electron atoms.

• The model is a convenient representation of the angular momenta of the electrons in the atom. Angular momentum is always split into orbital L, spin S and total J:

• {\displaystyle \mathbf {J} =\mathbf {L} +\mathbf {S} .}

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Answer 2

Thus the angle between L and S vector of electron is θ = 106.78 º

Explanation:

• Orbital spin and total angular moments are denoted by L, S and J respectively. Let's suppose
• If L=2,  S = 1, and J = 2,
• To find: the angle between L and S
• Now using vector atomic model of electron:

Solution:

J = L + S

J . J = |L|^2 + |S|^2 + 2|L|.|S| cosθ

So cosθ = [|J|^2 - |L|^2 - |S|^2] /  [2|L|.|S| ]

Now |L| = ([L (L+1)]^1 / 2 ) ħ

|S| = ([S (S + 1)]^1/2 ) ħ

|J| = ([J (J + 1 )]^1/2 ) ħ

So cosθ = [J (J + 1) - L ( L + 1) - S (S + 1)] / [2 ([L (L + 1)]^1/2 ) × ([S (S + 1)]^1/2 ) ]

Now cosθ = 6 - 6 - 2 / 2 × (6 × 2)^1/2

cosθ  = -0.2886

θ = 106.78º

Thus the angle between L and S vector of electron is θ = 106.78 º