Zeke Says That the Magnitude of the Orbital Angular Momentum $\ell\hbar$

question 26

Multiple Choice

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = $\ell\hbar$ .Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector $\vec { B }$ is $\sqrt { \ell ( \ell + 1 ) } \hbar$ .Which one,if either,is correct,and why?

• A)Ruth,because the maximum value of L is \(\sqrt { \ell ( \ell + 1 ) } \hbar\) .
• B)Ruth,because the orbital angular momentum always lines up with a magnetic field so that \(\overrightarrow { \mathbf { L } }\) has its maximum value along the field.
• C)Zeke,because the maximum magnitude of \(\overrightarrow { \mathbf { L } }\) is L = \(\ell\hbar\) .
• D)Zeke,because the orbital angular momentum always lines up with a magnetic field so that \(\overrightarrow { \mathbf { L } }\) has its maximum value along the field.
• E)Neither,because they have interchanged the maximum magnitude of \(\overrightarrow { \mathbf { L } }\) , \(\sqrt { \ell ( \ell + 1 ) } \hbar\) ,and \(\ell\hbar\) ,its maximum projection along a magnetic field direction.

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