Multiple Choice
How many energy sublevels are present in each of the first three principal energy levels (n = 1, 2, and 3) of a hydrogen atom?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
What is the maximum number of electrons that can have principal quantum number n = 3 and spin quantum number ms = +1/2?
A
9
B
12
C
6
D
18
Verified step by step guidance1
Recall that the principal quantum number \(n\) defines the energy level or shell of an electron. For \(n = 3\), the possible subshells are \(l = 0\) (3s), \(l = 1\) (3p), and \(l = 2\) (3d).
Determine the number of orbitals in each subshell using the formula: number of orbitals = \$2l + 1\(. For \)l = 0\(, orbitals = 1; for \)l = 1\(, orbitals = 3; for \)l = 2$, orbitals = 5.
Calculate the total number of orbitals for \(n = 3\) by summing the orbitals from all subshells: \$1 + 3 + 5 = 9$ orbitals.
Each orbital can hold a maximum of 2 electrons with opposite spins (\(m_s = +\frac{1}{2}\) and \(m_s = -\frac{1}{2}\)). Since we are only considering electrons with spin quantum number \(m_s = +\frac{1}{2}\), each orbital can hold only 1 such electron.
Multiply the total number of orbitals (9) by 1 electron per orbital with \(m_s = +\frac{1}{2}\) to find the maximum number of electrons with \(n = 3\) and \(m_s = +\frac{1}{2}\): \(9 \times 1 = 9\) electrons.
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