The difference between the orbital angular mo | vedclass

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Question

(A) The orbital angular momentum is given by the formula: $	ext{Orbital angular momentum} = \sqrt{\ell(\ell+1)} \frac{h}{2 \pi}$.For a $4f$ orbital,

Vedclass · Accepted Answer

$2 \sqrt{3} 	imes \frac{h}{2 \pi}$

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(A) The orbital angular momentum is given by the formula: $	ext{Orbital angular momentum} = \sqrt{\ell(\ell+1)} \frac{h}{2 \pi}$.For a $4f$ orbital, the azimuthal quantum number $\ell = 3$. Therefore, the orbital angular momentum is $\sqrt{3(3+1)} \frac{h}{2 \pi} = \sqrt{12} \frac{h}{2 \pi} = 2 \sqrt{3} \frac{h}{2 \pi}$.For a $4s$ orbital, the azimuthal quantum number $\ell = 0$. Therefore, the orbital angular momentum is $\sqrt{0(0+1)} \frac{h}{2 \pi} = 0$.The difference between the two is $2 \sqrt{3} \frac{h}{2 \pi} - 0 = 2 \sqrt{3} \frac{h}{2 \pi}$.

The difference between the orbital angular momentum of an electron in a $4f$ orbital and another electron in a $4s$ orbital is

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