Multiple Choice
How many electrons in an atom can have the quantum numbers n = 3 and l = 2?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
Determine the number of electrons that can have the following set of quantum numbers.
n = 4, l = 3, ml = – 1
A
2 e-
B
4 e-
C
6 e-
D
3 e-
Verified step by step guidance1
Understand the quantum numbers: n is the principal quantum number, l is the azimuthal quantum number, and ml is the magnetic quantum number. These numbers describe the energy level, shape, and orientation of an electron's orbital, respectively.
Identify the type of orbital: For n = 4 and l = 3, the orbital is a 4f orbital. The azimuthal quantum number l = 3 corresponds to an f orbital.
Determine the possible values of ml: The magnetic quantum number ml can range from -l to +l, including zero. For l = 3, ml can be -3, -2, -1, 0, 1, 2, 3.
Focus on the given ml value: The problem specifies ml = -1. This means we are considering only the orbitals with this specific orientation.
Determine the number of electrons: Each orbital can hold a maximum of 2 electrons with opposite spins. Therefore, for ml = -1, there can be 2 electrons.
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