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The permitted values of the total angular momentum quantum number, j, for an electron occupying an f orbital are
- a)7/2 and 5/2
- b)1/2 and -1/2
- c)9/2 and 7/2
- d)3/2 and 1/2
Correct answer is option 'A'. Can you explain this answer?
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The permitted values of the total angular momentum quantum number, j, ...
The total angular momentum vector then is the sum of the total orbital angular momentum vector and the total spin angular momentum vector.
J = L+S
The total angular momentum quantum number parameterizes the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). Due to the spin-orbit interaction in the atom, the orbital angular momentum no longer commutes with the Hamiltonian, nor does the spin.
For F orbital L value is 3 and there are two possible values for S i.e. +1/2 or –1/2.
⇒ J = L ± S
⇒ 3 ± 1/2
The permitted values of the total angular momentum quantum number, j, for an electron occupying an f orbital are 7/2 and 5/2.
J = L+S
The total angular momentum quantum number parameterizes the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). Due to the spin-orbit interaction in the atom, the orbital angular momentum no longer commutes with the Hamiltonian, nor does the spin.
For F orbital L value is 3 and there are two possible values for S i.e. +1/2 or –1/2.
⇒ J = L ± S
⇒ 3 ± 1/2
The permitted values of the total angular momentum quantum number, j, for an electron occupying an f orbital are 7/2 and 5/2.
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The permitted values of the total angular momentum quantum number, j, ...
Explanation:
Permitted values of total angular momentum quantum number, j, for an electron occupying an f orbital:
- The total angular momentum quantum number, j, for an electron occupying an f orbital can take on values that are half-integers of the form j = l + s, where l is the orbital angular momentum quantum number and s is the spin quantum number.
- For an f orbital, the orbital angular momentum quantum number, l, can take on values of 3, 2, 1, or 0.
- The spin quantum number, s, for an electron is always 1/2.
Calculating the permitted values of j:
- For l = 3, the possible values of j are 3/2 and 5/2 (j = 3/2 + 1/2, j = 3/2 + 1/2).
- For l = 2, the possible values of j are 5/2 and 3/2 (j = 2 + 1/2, j = 2 - 1/2).
- For l = 1, the possible values of j are 3/2 and 1/2 (j = 1 + 1/2, j = 1 - 1/2).
- For l = 0, the only possible value of j is 1/2 (j = 0 + 1/2).
Conclusion:
- Therefore, the permitted values of the total angular momentum quantum number, j, for an electron occupying an f orbital are 7/2 and 5/2, which corresponds to the values of l = 3.
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