Multiple Choice
Which of the following is the correct abbreviated electron configuration for nickel (atomic number 28)?
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10. Periodic Properties of the Elements
The Electron Configuration
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How many 5f orbitals are present in an atom?
A
5
B
7
C
9
D
3
Verified step by step guidance1
Recall that the number of orbitals in a given subshell is determined by the magnetic quantum number \( m_l \), which ranges from \( -l \) to \( +l \), where \( l \) is the azimuthal quantum number associated with the subshell.
Identify the value of \( l \) for the \( f \) subshell. For \( s, p, d, f \) orbitals, \( l = 0, 1, 2, 3 \) respectively. Therefore, for the \( f \) subshell, \( l = 3 \).
Calculate the number of possible \( m_l \) values for \( l = 3 \). Since \( m_l \) ranges from \( -3 \) to \( +3 \), the total number of orbitals is \( 2l + 1 = 2 \times 3 + 1 \).
Evaluate the expression \( 2l + 1 \) to find the number of \( f \) orbitals, which corresponds to the number of 5f orbitals in the atom (the principal quantum number \( n = 5 \) does not affect the number of orbitals in the subshell).
Conclude that the number of 5f orbitals is equal to the number of \( f \) orbitals, which is \( 7 \).
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