Q.35 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 35 Solution

Topic: Atoms & Nuclei · Official NTA Booklet Code 50

Question

In Geiger-Marsden experiment, the number of scattered α-particles N(θ) is plotted as a function of scattering angle θ. Which of the following options represents the correct plot?

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Verified Against NTA Final Answer Key

Option (3) : Plot (3): Steeply decreasing curve dropping precipitously from 10^7 at small angles down to 10-10^2 at large angles

📚 Atoms & Nuclei Easy

📋 Given Parameters & Problem Setup

Experiment Geiger-Marsden (Rutherford) alpha-particle scattering experiment

Variables Number of scattered alpha-particles N(theta) vs scattering angle theta (in degrees)

Vertical Axis Logarithmic scale from 10 to 10^7

Horizontal Axis Scattering angle from 0 to 180 degrees

⚡

The 30-Second Exam Hall Shortcut: ⚡ Rutherford Sin^4 Scattering Law

⏱️ Instant textbook recognition.

Number of particles scattered drops as 1 / sin^4(theta / 2)!

1 Rutherford formula: N(theta) is proportional to 1 / sin^4(theta / 2).

2 At near-zero angles (theta -> 0): sin(theta/2) is tiny, so N(theta) is enormous (~10^7). Almost all alpha particles pass straight through undeflected!

3 As theta increases beyond 90 degrees: sin(theta/2) reaches ~1, so N(theta) plummets to near zero (~10^1). Only about 1 in 8000 particles deflects backwards.

4 On a logarithmic plot, this produces a dramatic, hyperbola-like steep drop that flattens out near the baseline at large angles.

5 Directly matches Plot (3) in NCERT textbook. Solved in 5 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Rutherford scattering differential cross-section: dsigma/dOmega = [z*Z*e^2 / (4*pi*epsilon_0 * 4*E)]^2 * (1 / sin^4(theta/2)). The inverse fourth power of sine guarantees a steep drop-off.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

State Rutherford's Alpha-Particle Scattering Formula

In the Geiger-Marsden experiment, alpha particles scattered by a thin gold foil follow Rutherford's Coulombic scattering cross-section:

N(\theta) \propto \frac{1}{\sin^4\left(\frac{\theta}{2}\right)}

• theta is the scattering angle relative to the forward incident beam direction.
• N(theta) is the number of scattered alpha particles detected per unit area at angle theta.

Step 2

Analyze Angle Regimes (Small vs Large Angles)

Evaluate the theoretical scattering count across the angular domain [0, 180] degrees:

\theta \to 0^\circ \implies \sin\left(\frac{\theta}{2}\right) \to 0 \implies N(\theta) \approx 10^7, \qquad \theta = 180^\circ \implies \sin(90^\circ) = 1 \implies N(180^\circ) \approx 10

• At small angles (< 20 degrees), the vast majority of particles suffer negligible deflection.
• At large angles (> 90 degrees), head-on collisions with the massive nucleus are extraordinarily rare (~1 in 8000).

Step 3

Identify the Correct Graph in the Question Options

Match the qualitative behavior to the provided plots:

\text{Plot (3): Steep hyper-exponential drop from } 10^7 \text{ down to } 10^1 \text{ over } [0^\circ, 180^\circ]

• Plot (1) shows a straight upward line (completely unphysical).
• Plot (2) shows an inverted curve that stays high until 90 degrees (false).
• Plot (4) shows a bell-shaped Gaussian peak at 90 degrees (false).
• Matches Plot (3) perfectly.

⭐

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 Option (1)

✗ Incorrect

Verdict & Scientific Reason:

Completely unphysical.

⚠️

Student Fallacy (Why candidates pick this trap): Assumes more particles scatter at larger angles.

Note: Scattering drops dramatically with angle; it never increases.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Fails to capture sharp forward peak.

⚠️

Student Fallacy (Why candidates pick this trap): Believes scattering remains constant across small and medium angles.

Note: The 1/sin^4(theta/2) drop begins immediately at 10–20 degrees.

3 Option (3)

✓ 100% Correct

Verdict & Scientific Reason:

Canonical textbook graph from Geiger-Marsden experiment; confirmed by Official NTA Key.

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Why this is airtight: Flawless recall of Rutherford's inverse fourth power scattering law.

Note: Exact atomic physics.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Confuses scattering with blackbody radiation or diffraction envelope.

⚠️

Student Fallacy (Why candidates pick this trap): Assumes maximum scattering occurs symmetrically at 90 degrees.

Note: Minimum particles scatter at large angles; there is no peak at 90 degrees.

⚠️

NTA Trap Alert: Confusing Atomic Scattering with Diffraction Central Maximum

Students who confuse Rutherford scattering with wave optics or blackbody radiation pick the bell curve in Plot (4).

🛡️ How to avoid the -1 mark: Remember Rutherford's famous quote: "It was as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you!" Backward deflection is virtually zero, so the graph must drop to the baseline.

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Core NEET Syllabus Standard

NEET UG Physics Core Standards · Atoms Standard Benchmark

Core Scientific Principle Tested:

"Rutherford scattering: N(theta) is proportional to 1 / sin^4(theta/2). The steep decline confirms that the atom is mostly empty space with a tiny, dense, positively charged nucleus."

Syllabus Focus: Alpha-Particle Scattering Experiment & Rutherford's Nuclear Model

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 35 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Rutherford Sin^4 Scattering Law

Step-by-Step Rigorous Workflow & Mathematical Proof

State Rutherford's Alpha-Particle Scattering Formula

Analyze Angle Regimes (Small vs Large Angles)

Identify the Correct Graph in the Question Options

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Atomic Scattering with Diffraction Central Maximum

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Atoms & Nuclei

Bohr Orbit Radius from Orbital Velocity in an Excited Hydrogen Atom

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