GRE Physics GR 1777 Problem Solution
012. Quantum Mechanics (Quantum number)
The magnetic quantum number $latex m_{l}$ can be determined as
$latex m_l = -l, -(l+1), .., -1, 0, 1, .., +(l-1), +l$
Thus, the number of allowed values of $latex m_l$ is
$latex N_{m_{l}} = (2l + 1)$.
Therefore, when $latex l = 2$, the number of allowed values of $latex m_l$ is 5.
Answer
(E)
References
https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantum_Numbers
https://en.wikipedia.org/wiki/Magnetic_quantum_number
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