We’re being asked to find what is the maximum number of electrons given the quantum numbers, n = 4, m l = -3, m s = +1/2
Recall that the quantum numbers that define an electron are:
• Principal Quantum Number (n): deals with the size and energy of the atomic orbital. The possible values for n are 1 to ∞.
• Angular Momentum Quantum Number (l): deals with the shape of the atomic orbital. The possible values for l are 0 to n – 1.
• Magnetic Quantum Number (ml): deals with the orientation of the atomic orbital in 3D space. The possible values for ml are the range of –l to +l.
• Spin Quantum Number (ms): deals with the spin of the electron. The possible values for ms are either –1/2 (spin down) or +1/2 (spin up).
The maximum number of electrons in an atom that can have the following set of quantum numbers is:
n = 4, m l = -3, m s = +1/2
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