Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = .Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector is .Which one, if either, is correct, and why?
A)Ruth, because the maximum value of L is
B)Ruth, because the orbital angular momentum always lines up with a magnetic field so that has its maximum value along the field.
C)Zeke, because the maximum magnitude of is L =
D)Zeke, because the orbital angular momentum always lines up with a magnetic field so that has its maximum value along the field.
E)Neither, because they have interchanged the maximum magnitude of , , and , its maximum projection along a magnetic field direction.

Question

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = .Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector is .Which one, if either, is correct, and why?   
A)Ruth, because the maximum value of L is 
B)Ruth, because the orbital angular momentum always lines up with a magnetic field so that has its maximum value along the field. 
C)Zeke, because the maximum magnitude of is L = 
D)Zeke, because the orbital angular momentum always lines up with a magnetic field so that has its maximum value along the field. 
E)Neither, because they have interchanged the maximum magnitude of , , and , its maximum projection along a magnetic field direction.

Quizplus · Accepted Answer

Zeke and Ruth have interchanged the meanings of orbital angular momentum (L) and its projection along a magnetic field direction (magnetic quantum number, m). The magnitude of L in the hydrogen atom is given by $L = \sqrt{l(l+1)}\hbar$, where l is the orbital quantum number and $\hbar$ is the reduced Planck constant. The maximum value of L occurs when l has its maximum value, which is n-1, where n is the principal quantum number (the energy level of the electron). So, the maximum value of L is $\sqrt{(n-1)n}\hbar$.

The maximum magnitude of the projection of L along a magnetic field direction is given by $m\hbar$, where m can have values from -l to l in integer steps. So, the maximum value of $m\hbar$ occurs when m has its maximum value, which is equal to l. Therefore, the maximum magnitude of the projection of L along a magnetic field direction is equal to $\sqrt{l(l+1)}\hbar$.

Therefore, neither Zeke nor Ruth is correct, and the correct answer is E, which states that they have interchanged the maximum values of L and its projection along a magnetic field direction.

Zeke Says That the Magnitude of the Orbital Angular Momentum