Textbook Question
What is the maximum number of electrons in an atom that can have the following quantum numbers? a. n = 3, ml = -2; b. n = 4, l = 3; c. n = 5, l = 3, ml = 2; d. n = 4, l = 1, ml = 0.
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
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Determine the number of electrons that can have the following set of quantum numbers.
n = 4, mL = – 1, ms = –1/2
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, mL is the magnetic quantum number, and ms is the spin quantum number.
The principal quantum number n = 4 indicates the fourth energy level, which can have s, p, d, and f subshells.
The magnetic quantum number mL = -1 specifies the orientation of the orbital within a subshell. For p orbitals (l = 1), mL can be -1, 0, or +1. For d orbitals (l = 2), mL can be -2, -1, 0, +1, or +2.
The spin quantum number ms = -1/2 indicates the spin of the electron. Each orbital can hold two electrons with opposite spins: +1/2 and -1/2.
Determine the number of electrons: For mL = -1 and ms = -1/2, each orbital with mL = -1 can hold one electron with ms = -1/2. Count the orbitals with mL = -1 in the n = 4 level (4p and 4d subshells) to find the total number of electrons.
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