Number of Nodes: Radial, Angular and Total Formula (NEET)
Chemistry · Structure Of Atom · NEET
A node is a place where the chance of finding the electron is zero. Use three formulas: Angular nodes = l, Radial nodes = n − l − 1, and Total nodes = n − 1. Memory hook: "Angular = l, Total = n − 1, Radial is what is left over (n − l − 1)."
The three node formulas at a glance: Angular nodes = l (set by subshell shape), Radial nodes = n − l − 1 (spherical shells by distance), and Total nodes = n − 1. For a 4f orbital this gives 3 angular, 0 radial, and 3 total nodes.
Your doubts, answered
What exactly is a node in simple words?
A node is a region where the probability of finding the electron is zero. The wave function psi becomes zero there, so psi-squared (probability) is also zero. Think of it as a 'dead zone' inside the orbital where the electron never sits. For NEET you only need to count how many of these dead zones an orbital has.
What is the formula for radial, angular and total nodes?
Three simple formulas. Angular nodes = l (the azimuthal quantum number). Radial nodes (also called spherical nodes) = n − l − 1. Total nodes = n − 1. Notice that Angular + Radial = l + (n − l − 1) = n − 1 = Total. So the three always fit together.
How do I know the value of l for s, p, d, f?
l is fixed by the subshell letter: s means l = 0, p means l = 1, d means l = 2, f means l = 3. So the number of angular nodes is 0 for s, 1 for p, 2 for d, and 3 for f. This value never changes, no matter what n is.
What is the difference between a radial node and an angular node?
An angular node is a flat plane (or cone) passing through the nucleus that decides the SHAPE of the orbital, so angular nodes = l. A radial node is a spherical shell at a certain distance where psi = 0, so it depends on how far the electron is from the nucleus. Radial nodes = n − l − 1. Angular = shape, Radial = distance.
How many nodes does a 3d orbital have?
For 3d, n = 3 and l = 2. Angular nodes = l = 2. Radial nodes = n − l − 1 = 3 − 2 − 1 = 0. Total nodes = n − 1 = 2. So a 3d orbital has 2 angular nodes, 0 radial nodes, and 2 total nodes.
How many nodes does a 3s orbital have?
For 3s, n = 3 and l = 0. Angular nodes = l = 0 (all s orbitals are spherical, no plane). Radial nodes = n − l − 1 = 3 − 0 − 1 = 2. Total nodes = n − 1 = 2. So a 3s orbital has 0 angular nodes and 2 radial nodes. This is why the 3s radial plot crosses zero twice.
Why is total nodes equal to n minus 1?
Because total nodes = angular nodes + radial nodes = l + (n − l − 1). The l cancels out and you are left with n − 1. This is exactly what NCERT states: the total number of nodes is (n − 1), made of l angular nodes and (n − l − 1) radial nodes.
⚠️ The NEET trap ✗ Students see 'nodes' and reflexively write n − 1 for every type, or mix up which formula gives radial vs angular. For '3 angular nodes and 3 total nodes' they pick 3d or 5p by guessing. ✓ Read the words carefully. Angular nodes = l = 3 means an f subshell. Total nodes = n − 1 = 3 means n = 4. So the orbital is 4f. Always translate: angular → l, total → n − 1, then find n and l. 🧠 Angular tells you the LETTER (l), Total tells you the NUMBER (n). 3 angular + 3 total = 4f.
Real NEET questions
NEET 2019 (Odisha)
An orbital having 3 angular nodes and 3 total nodes is:
A · 5p
B · 3d
C · 4f ✓
D · 6d
Solution: Angular nodes = l = 3, which means an f subshell. Total nodes = n − 1 = 3, so n = 4. Therefore the orbital is 4f. (Check radial nodes = n − l − 1 = 4 − 3 − 1 = 0, and 0 + 3 = 3 total. Correct.)
ReNEET 2026
Consider schematic plots of the radial wave function psi(r) against distance r. The plot representing two radial nodes is the one where psi crosses zero twice. Which orbital has 2 radial nodes among s orbitals?
A · 1s
B · 2s
C · 3s ✓
D · 2p
Solution: Radial nodes = n − l − 1. For an s orbital l = 0, so radial nodes = n − 1. To get 2 radial nodes we need n − 1 = 2, so n = 3. That is the 3s orbital, whose psi(r) curve crosses the axis twice. (1s = 0, 2s = 1, 3s = 2 radial nodes.)
NEET 2017 & 2018
Which one is a wrong statement?
A · The electronic configuration of N atom is 1s2 2s2 2px1 2py1 2pz1 ✓
B · An orbital is designated by three quantum numbers while an electron by four
C · Total orbital angular momentum of an electron in an s orbital is zero
D · The value of m for d(z^2) is zero
Solution: Per the official key, (A) is treated as the wrong statement. The others are correct: an orbital needs three quantum numbers (n, l, m) and an electron four; for an s orbital l = 0 so orbital angular momentum sqrt(l(l+1))·h/2pi = 0 (this links to angular nodes = l = 0); and m = 0 for d(z^2). This shows how l = 0 for s makes both angular nodes and angular momentum zero.
Solved Structure Of Atom NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Total nodes = n − 1, where n is the principal quantum number. This equals the sum of angular nodes (l) and radial nodes (n − l − 1).
Do all s orbitals have zero angular nodes?
Yes. For any s orbital l = 0, so angular nodes = l = 0. That is why every s orbital is spherical. Their nodes are all radial (n − 1 of them).
Can the number of nodes be a fraction or negative?
No. Nodes are always whole numbers (0, 1, 2, ...). If your formula gives a negative or non-integer answer, you have used a wrong n or l. For example, 1s gives n − l − 1 = 1 − 0 − 1 = 0 radial nodes, which is correct.
Is a radial node the same as a spherical node?
Yes. Radial nodes are also called spherical nodes because they are spherical shells at fixed distances from the nucleus where psi = 0. Angular nodes are also called nodal planes.
How many total nodes are in a 4d orbital?
For 4d, n = 4 and l = 2. Total nodes = n − 1 = 3. Angular nodes = 2, radial nodes = n − l − 1 = 1. Check: 2 + 1 = 3.
