The quantum mechanical model of the hydrogen atom requires that if the principal quantum number = 5,there will be how many permitted orbital magnetic quantum numbers?
A)4
B)5
C)10
D)9
E)11

Question

The quantum mechanical model of the hydrogen atom requires that if the principal quantum number = 5,there will be how many permitted orbital magnetic quantum numbers?
A)4
B)5
C)10
D)9
E)​11

Quizplus · Accepted Answer

The orbital magnetic quantum number (ml) can range from -l to +l, including 0, where l is the azimuthal quantum number. For a principal quantum number (n) of 5, l can be 0, 1, 2, 3, and 4. For each l value, the ml values range as follows: for l=0, ml=0 (1 value); for l=1, ml=-1, 0, 1 (3 values); for l=2, ml=-2, -1, 0, 1, 2 (5 values); for l=3, ml=-3, -2, -1, 0, 1, 2, 3 (7 values); for l=4, ml=-4, -3, -2, -1, 0, 1, 2, 3, 4 (9 values). Adding these up gives 1+3+5+7+9 = 25, but the question seems to have a mistake in its formulation or choices. Based on standard quantum mechanics, the correct calculation should consider the total number of ml values across all possible l values for n=5, which indeed would sum up to more than any of the provided options. However, if we interpret the question as asking for the number of ml values for the highest l value (l=4), then the correct answer would be 9, corresponding to ml values from -4 to +4.

The Quantum Mechanical Model of the Hydrogen Atom Requires That