Multiple Choice
Which of the following sets lists all possible values of the angular momentum quantum number l for the principal quantum number n = 3?
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9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
Multiple Choice
In a ground state atom of argon (Ar), how many electrons have the angular momentum quantum number l = 0?
A
10
B
6
C
8
D
2
Verified step by step guidance1
Recall that the angular momentum quantum number \( l \) defines the shape of the orbital: \( l = 0 \) corresponds to s orbitals.
Determine the electron configuration of argon (Ar), which has 18 electrons. The configuration is: \( 1s^2 2s^2 2p^6 3s^2 3p^6 \).
Identify all electrons in orbitals where \( l = 0 \), i.e., all electrons in s orbitals. These are the electrons in the \( 1s \), \( 2s \), and \( 3s \) orbitals.
Count the electrons in each s orbital: \( 1s^2 \) has 2 electrons, \( 2s^2 \) has 2 electrons, and \( 3s^2 \) has 2 electrons, totaling 6 electrons so far.
Note that p orbitals have \( l = 1 \), so they do not count. Therefore, the total number of electrons with \( l = 0 \) is the sum of electrons in all s orbitals, which is 6.
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