Textbook Question
How many nodal surfaces does a 4s orbital have? Draw a cutaway representation of a 4s orbital showing the nodes and the regions of maximum electron probability.
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9. Quantum Mechanics
Quantum Numbers: Nodes
Multiple Choice
For a 3p orbital, how many radial nodes are present?
A
0
B
1
C
2
D
3
Verified step by step guidance1
Recall that the number of radial nodes in an atomic orbital is given by the formula: \(\text{Number of radial nodes} = n - l - 1\), where \(n\) is the principal quantum number and \(l\) is the azimuthal (angular momentum) quantum number.
Identify the quantum numbers for the given orbital: For a 3p orbital, \(n = 3\) (since it is the third energy level) and \(l = 1\) (since \(l = 0\) corresponds to s, \(l = 1\) to p, \(l = 2\) to d, etc.).
Substitute the values into the formula: \(\text{Number of radial nodes} = 3 - 1 - 1\).
Simplify the expression to find the number of radial nodes: \$3 - 1 - 1 = 1$.
Conclude that a 3p orbital has 1 radial node.
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