Which atomic orbital has the fewest angular nodes?  

• A. 3d
• B. 4p
• C. 7s
• D. 5d
• E. 6f

Answer: (C)

Verified step by step guidance

1. Understand the concept of angular nodes: Angular nodes are regions around the nucleus where the probability of finding an electron is zero. The number of angular nodes is determined by the orbital type (s, p, d, f).
2. Recall the formula for angular nodes: The number of angular nodes is given by the formula \( l \), where \( l \) is the azimuthal quantum number. For s, p, d, and f orbitals, \( l \) values are 0, 1, 2, and 3 respectively.
3. Determine the angular nodes for each orbital: Calculate the angular nodes for each given orbital using the \( l \) value. For example, a 3d orbital has \( l = 2 \), so it has 2 angular nodes.
4. Compare the angular nodes: Compare the number of angular nodes for each orbital listed (3d, 4p, 7s, 5d, 6f) to identify which has the fewest angular nodes.
5. Identify the orbital with the fewest angular nodes: Based on the comparison, determine which orbital has the smallest number of angular nodes, which corresponds to the smallest \( l \) value.