Q.18 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 18 Solution

Topic: Dual Nature of Matter & Radiation · Official NTA Booklet Code 50

Question

A ray of light with wavelength λ is incident on three different photo-electric cells namely 1, 2 and 3. The threshold wavelength of these photo-electric cells are λ₁, λ₂ and λ₃, respectively and the magnitude of stopping potentials of these cells are V₁, V₂ and V₃, respectively. The relation between λ and threshold wavelengths are λ₁ < λ, λ₂ > λ and λ₃ >> λ. The correct option is:

✓

Verified Against NTA Final Answer Key

Option (1) : V_1 = 0, V_2 < V_3

📚 Dual Nature of Matter & Radiation Medium

📋 Given Parameters & Problem Setup

Incident Light Wavelength lambda

Cell 1 Threshold Wavelength lambda_1 < lambda (incident wavelength exceeds threshold)

Cell 2 Threshold Wavelength lambda_2 > lambda (photoelectric emission occurs)

Cell 3 Threshold Wavelength lambda_3 >> lambda (photoelectric emission occurs with very low work function)

Stopping Potentials V_1, V_2, V_3

⚡

The 30-Second Exam Hall Shortcut: ⚡ Threshold Wavelength Cutoff Rule

⏱️ Bypasses numerical evaluations.

Emission requires lambda <= lambda_th; Larger lambda_th means higher stopping potential!

1 Photoelectric condition in wavelength: Photon energy hc/lambda must be >= hc/lambda_th ==> lambda <= lambda_th.

2 For Cell 1: lambda_1 < lambda ==> lambda > lambda_1. Incident wavelength is LONGER than threshold, meaning photon energy is insufficient. NO emission occurs ==> V_1 = 0!

3 For Cells 2 and 3: lambda < lambda_2 and lambda << lambda_3. Emission occurs in both.

4 Stopping potential: e*V_0 = hc * (1/lambda - 1/lambda_th).

5 Since lambda_3 >> lambda_2, 1/lambda_3 is much smaller than 1/lambda_2, meaning work function Phi_3 is smaller than Phi_2.

6 Smaller work function leaves GREATER kinetic energy: V_3 > V_2 (or V_2 < V_3).

7 Combine results: V_1 = 0 and V_2 < V_3. Matches Option (1) in 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Einstein's Photoelectric Equation: e*V_0 = hc/lambda - Phi. Since Phi = hc/lambda_th, higher threshold wavelength implies a smaller work function, which directly increases stopping potential.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Evaluate Photoelectric Threshold Condition for Cell 1

For photoelectric emission to occur, incident photon energy must equal or exceed the work function:

E = \frac{hc}{\lambda} \ge \Phi = \frac{hc}{\lambda_{\text{th}}} \iff \lambda \le \lambda_{\text{th}}

• For Cell 1, we are given lambda_1 < lambda, which means lambda > lambda_1.
• The incident wavelength exceeds threshold wavelength; photon energy is strictly below the work function.
• No photoelectrons are ejected, so the stopping potential is identically zero: V_1 = 0.

Step 2

Compare Stopping Potentials for Cells 2 and 3

For Cells 2 and 3, lambda < lambda_2 and lambda << lambda_3, so photoelectric emission takes place in both cells:

e V_0 = K_{\text{max}} = hc \left( \frac{1}{\lambda} - \frac{1}{\lambda_{\text{th}}} \right)

• eV_2 = hc (1/lambda - 1/lambda_2).
• eV_3 = hc (1/lambda - 1/lambda_3).
• Given lambda_3 >> lambda_2 > lambda, we have 1/lambda_3 < 1/lambda_2.
• Subtracting a smaller number yields a larger difference: (1/lambda - 1/lambda_3) > (1/lambda - 1/lambda_2).

Step 3

Conclude the Inequality Ordering

Compare the stopping potential magnitudes:

V_3 > V_2 \iff V_2 < V_3

• Combining with V_1 = 0 yields: V_1 = 0, V_2 < V_3.
• Matches Option (1) exactly.

⭐

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)

✓ 100% Correct

Verdict & Scientific Reason:

100% scientifically sound; confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Correctly applies inverse wavelength cutoff and work function comparison.

Note: Flawless physics.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Inverts the work function relationship.

⚠️

Student Fallacy (Why candidates pick this trap): Assumes larger threshold wavelength means larger work function and lower stopping potential.

Note: Work function Phi = hc/lambda_th is inversely proportional to threshold wavelength!

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Reverses threshold condition.

⚠️

Student Fallacy (Why candidates pick this trap): Confuses threshold wavelength with threshold frequency, thinking lambda > lambda_th causes emission.

Note: Longer wavelength means LESS energy, not more.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Double misconception.

⚠️

Student Fallacy (Why candidates pick this trap): Believes Cell 3 fails to emit photoelectrons.

Note: Cell 3 has the longest threshold wavelength and therefore the easiest emission.

⚠️

NTA Trap Alert: Frequency vs Wavelength Cutoff Inversion

Many candidates confuse nu >= nu_0 with lambda >= lambda_0. For wavelength, emission ONLY occurs when lambda <= lambda_th!

🛡️ How to avoid the -1 mark: Anchor photon energy: E = hc/lambda. As wavelength increases, photon energy drops! Hence, lambda must be LESS than or equal to threshold.

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Dual Nature of Radiation and Matter Standard Benchmark

Core Scientific Principle Tested:

"Photoelectric emission occurs only if lambda <= lambda_th. Stopping potential is e*V_0 = hc*(1/lambda - 1/lambda_th)."

Syllabus Focus: Photoelectric Equation, Threshold Wavelength, and Stopping Potential

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 18 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Threshold Wavelength Cutoff Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Evaluate Photoelectric Threshold Condition for Cell 1

Compare Stopping Potentials for Cells 2 and 3

Conclude the Inequality Ordering

360° Option Elimination Engine Key Feature

NTA Trap Alert: Frequency vs Wavelength Cutoff Inversion

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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