An electron in a hydrogen atom is described by the quantum numbers: n = 7 and m_l = 4. What are the possible values for the orbital quantum number ? A)only 0 or 4 B)only 4 or 7 C)only 5 or 6 D)only 4, 5, or 6 E)only 5, 6, or 7

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The value of l can range from 0 to n - 1. Therefore, for n = 7, the valid values of l are 0, 1, 2, 3, 4, 5, and 6. The value of mS can only be -1/2 or 1/2, which does not affect the possible values of l. However, the given value of m_l, which represents the magnetic quantum number, does affect the possible values of l. m_l = 4 corresponds to the value of ml, which can range from -l to l. Therefore, we have: ml = 4 -4 ≤ ml ≤ 4 From these inequalities, we can deduce that the possible values of l are 4, 5, and 6. Therefore, the answer is D, only 4, 5, or 6.

An Electron in a Hydrogen Atom Is Described by the Quantum