Q.88 Chemistry ⭐ 360° Option Elimination Active

NEET 2026 Chemistry Question 88 Solution

Topic: Structure of Atom · Official NTA Booklet Code 50

Question

Consider the following schematic plots of orbital wavefunction (ψr) against distance (r) from the nucleus. The figure representing two radial nodes in the orbital is

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Verified Against NTA Final Answer Key

Option (3) : C

📚 Structure of Atom Medium

📋 Given Parameters & Problem Setup

Plots Orbital wavefunction (ψ_r) against distance (r) from nucleus

Plot A Monotonically decreasing from positive value to zero (0 radial nodes, 1s)

Plot B Starts positive, crosses zero once into negative region (1 radial node, 2s)

Plot C Starts positive, crosses zero twice (+ → - → +) (2 radial nodes, 3s)

Plot D Starts at zero at r=0, crosses zero once (1 radial node, 3p or 4d)

Target The figure representing two radial nodes

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The 30-Second Exam Hall Shortcut: ⚡ Count Zero Crossings at r > 0

⏱️ Save ~50 seconds

A radial node is a point where the wavefunction ψ_r crosses zero at finite distance r > 0!

1 Examine Plot A: Never crosses zero (0 radial nodes).

2 Examine Plot B: Crosses the zero line once (1 radial node).

3 Examine Plot C: Drops below zero line (1st node), curves up and crosses zero line again (2nd node)! Exactly TWO radial nodes!

4 Examine Plot D: Starts at origin (r=0 is an angular node origin, not radial), crosses once (1 radial node).

5 Plot C is the unequivocal match for two radial nodes! Pick Option (3) in 10 seconds!

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Why You Can 100% Trust This Shortcut: Schrödinger wave mechanics: The number of radial nodes in an orbital equals (n - l - 1). A 3s orbital has n=3, l=0 ⇒ 3 - 0 - 1 = 2 radial nodes, perfectly matching curve C.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Define Radial Nodes in Quantum Mechanical Wavefunctions

A radial node is a spherical surface around the nucleus at a finite distance r > 0 where the radial wavefunction ψ_r (and consequently the radial probability density ψ_r²) passes through zero.

\text{Number of Radial Nodes} = n - l - 1

• Graphically, each radial node corresponds to the wavefunction curve crossing the r-axis (zero-line) at r > 0.

Step 2

Analyze Each Plot in the Question

1. Plot A: ψ_r has a non-zero maximum at r = 0 and decays asymptotically to zero without ever cutting the zero line. Number of radial nodes = 0 (Represents 1s orbital). 2. Plot B: ψ_r starts positive at r = 0, crosses the zero axis once, dips into a negative minimum, and approaches zero asymptotically. Number of radial nodes = 1 (Represents 2s orbital). 3. Plot C: ψ_r starts positive at r = 0, crosses the zero axis first into negative values, turns around and crosses the zero axis a second time into positive values, and then approaches zero asymptotically. Number of radial nodes = 2 (Represents 3s orbital). 4. Plot D: ψ_r starts at 0 at r = 0 (since l > 0), rises to a positive peak, crosses the zero axis once into negative, and approaches zero. Number of radial nodes = 1 (Represents 3p or 4d orbital).

\text{Plot C has exactly 2 zero-crossings} \implies 2\text{ radial nodes}

• Plot C represents 2 radial nodes.

Step 3

Conclusion

The figure representing two radial nodes is C.

\text{Matches Option (3)}

• Matches Option (3).

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360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Plot A has zero radial nodes (1s orbital).

⚠️

Student Fallacy (Why candidates pick this trap): Confusing asymptotic tail with a node.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Plot B has only one radial node (2s orbital).

⚠️

Student Fallacy (Why candidates pick this trap): Counting the negative peak as a node.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

Scientifically exact: Curve C crosses the zero axis at two distinct points, representing exactly two radial nodes (e.g. 3s orbital).

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Why this is airtight: None; precise graphical interpretation of radial wavefunctions.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Plot D crosses zero only once at finite r (1 radial node for an orbital with l > 0).

⚠️

Student Fallacy (Why candidates pick this trap): Counting the origin r = 0 as a radial node.

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NTA Trap Alert: Counting the Origin (r = 0) as a Radial Node

For p, d, and f orbitals, the wavefunction starts at zero at the nucleus (r = 0). Students mistakenly count r = 0 as a radial node. By quantum mechanical definition, radial nodes are strictly located at finite, non-zero distances (r > 0)!

🛡️ How to avoid the -1 mark: Never count r = 0. Only count points where the curve CROSSES the zero line at r > 0.

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Core NEET Syllabus Standard

NEET Chemistry Core Syllabus · Structure of Atom Standard Benchmark

Core Scientific Principle Tested:

"Radial nodes correspond to points where the radial wavefunction ψ_r changes sign (crosses zero)."

Syllabus Focus: Radial wavefunctions and radial probability distribution curves

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Cross the line once = 1 node; Cross the line twice = 2 nodes on Curve C!

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NEET 2026 Chemistry Question 88 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Count Zero Crossings at r > 0

Step-by-Step Rigorous Workflow & Mathematical Proof

Define Radial Nodes in Quantum Mechanical Wavefunctions

Analyze Each Plot in the Question

Conclusion

360° Option Elimination Engine Key Feature

NTA Trap Alert: Counting the Origin (r = 0) as a Radial Node

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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