The quantum mechanical model of the hydrogen atom requires that if the principal quantum number = 3,there will be permitted how many orbital magnetic quantum numbers?
A) 2
B) 3
C) 6
D) 5
E) 7

Question

The quantum mechanical model of the hydrogen atom requires that if the principal quantum number = 3,there will be permitted how many orbital magnetic quantum numbers?
A) 2
B) 3
C) 6
D) 5
E) ​7

Quizplus · Accepted Answer

For a given principal quantum number n, the possible values of the azimuthal quantum number l range from 0 to n-1. For n=3, l can be 0, 1, or 2. The magnetic quantum number m_l ranges from -l to +l, giving 1, 3, and 5 values respectively for l=0, 1, and 2. Therefore, the total number of magnetic quantum numbers is 1 + 3 + 5 = 9. However, the question seems to be asking for the number of distinct m_l values for l=2, which is 5.

The Quantum Mechanical Model of the Hydrogen Atom Requires That