Multiple Choice
Which quantum number is most important in determining the size of an atomic orbital?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
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How many d orbitals exist in a single energy level where the principal quantum number n = 3 of an atom?
A
3
B
10
C
5
D
7
Verified step by step guidance1
Recall that the number of orbitals in a subshell depends on the azimuthal quantum number \( l \). For d orbitals, \( l = 2 \).
The number of orbitals for a given \( l \) is given by the formula \( 2l + 1 \).
Substitute \( l = 2 \) into the formula: \( 2(2) + 1 = 5 \).
Therefore, there are 5 d orbitals in any energy level that contains a d subshell.
Since \( n = 3 \) includes the d subshell (because \( l \) can be 0, 1, or 2 for \( n = 3 \)), the number of d orbitals at \( n = 3 \) is 5.
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