For the 2p_x orbital, how many spherical nodes and planar nodes are present?

• A. 0 spherical nodes, 0 planar nodes
• B. 1 spherical node, 1 planar node
• C. 0 spherical nodes, 1 planar node
• D. 1 spherical node, 0 planar nodes

Answer: (C)

Verified step by step guidance

1. Recall that the total number of nodes in an atomic orbital is given by the formula: \(n - 1\), where \(n\) is the principal quantum number.
2. For the 2p\_x orbital, the principal quantum number \(n\) is 2, so the total number of nodes is \$2 - 1 = 1$.
3. Nodes can be either spherical (radial) nodes or planar (angular) nodes. Spherical nodes are spherical surfaces where the probability density is zero, while planar nodes are planes where the wavefunction changes sign.
4. For p orbitals (where the azimuthal quantum number \(l = 1\)), there are no spherical nodes because spherical nodes correspond to \(n - l - 1\) and here it is \$2 - 1 - 1 = 0$ spherical nodes.
5. Since the total number of nodes is 1 and there are 0 spherical nodes, the remaining node must be a planar node. Therefore, the 2p\_x orbital has 0 spherical nodes and 1 planar node.