Radial And Angular Nodes
For a 3d orbital in a hydrogen-like atom, what are the numbers of radial nodes and angular nodes respectively?
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About This Question
- Subject
- chemistry
- Chapter
- atomic structure
- Topic
- radial and angular nodes
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
0, 2
The number of radial nodes in an orbital is given by n - l - 1, and the number of angular nodes equals l. For the 3d orbital, n=3 and l=2. Therefore: radial nodes = n - l - 1 = 3 - 2 - 1 = 0; angular nodes = l = 2. This gives 0 radial nodes and 2 angular nodes. Option 1, 2 is incorrect; it would require a radial node count of 1, which means n - l - 1 = 1, giving n = 4 for l=2, corresponding to a 4d orbital not 3d. Option 2, 0 is incorrect because it has l=0 (s orbital) and n - 0 - 1 = 2, giving a 3s orbital. Option 0, 3 is incorrect; l=3 corresponds to an f orbital, not d. Total nodes in any orbital always equal n - 1, which for 3d is 3 - 1 = 2, consistent with 0 radial + 2 angular = 2. This node counting formula is an important NCERT concept tested regularly in JEE. Plausibility check: total nodes = radial + angular = 0 + 2 = 2 = n - 1 = 3 - 1 = 2, confirming correctness.
This easy difficulty chemistry question is from the chapter atomic structure, covering the topic of radial and angular nodes. It appeared in the 2025 exam.
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