Q.16 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 16 Solution

Topic: Dual Nature of Radiation and Matter · Official NTA Booklet Code G5

Question

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to:

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Verified Against NTA Final Answer Key

Option (3) : 1 / V

📚 Dual Nature of Radiation and Matter Easy

📋 Given Parameters & Problem Setup

Accelerating Potential V volts

Physical Quantity Minimum cutoff wavelength of X-rays (λ_min)

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The 30-Second Exam Hall Shortcut: ⚡ Duane-Hunt Inverse Voltage Law (12400 / V Å)

⏱️ Save ~30 seconds

Maximum photon energy equals kinetic energy of electron: hc/λ_min = eV → λ_min = hc/(eV) ∝ 1/V in 5 seconds!

1 Recall Duane-Hunt law: an electron accelerated through potential V gains kinetic energy K = eV.

2 The most energetic X-ray photon emitted when the electron is fully stopped in a single collision has energy E_max = hν_max = hc / λ_min.

3 Equate: hc / λ_min = eV.

4 Rearrange: λ_min = hc / (e V) ∝ 1 / V.

5 Immediately pick Option (3) without confusing with de Broglie wavelength (which is 1/√V)!

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Why You Can 100% Trust This Shortcut: Fundamental Quantum Physics · Duane-Hunt Relation (Cutoff continuous X-ray wavelength: λ_min = hc / (eV) ∝ 1/V).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Kinetic Energy of Accelerated Electron

An electron of charge e accelerated from rest through potential difference V acquires kinetic energy:

K = e V

Step 2

Maximum Photon Energy and Cutoff Wavelength

In continuous X-ray production (Bremsstrahlung), the minimum wavelength λ_min corresponds to the maximum photon energy, occurring when the entire kinetic energy of the electron is transferred to a single photon in a single collision:

E_{\text{max}} = h \nu_{\text{max}} = \frac{h c}{\lambda_{\text{min}}} = e V

Step 3

Proportionality Derivation

Solve for λ_min in terms of potential difference V:

\lambda_{\text{min}} = \frac{h c}{e V} \implies \lambda_{\text{min}} \propto \frac{1}{V}

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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 (1)

✗ Incorrect

Verdict & Scientific Reason:

Quadratic dependence is physically baseless.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate mixed up energy formulas.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Direct square-root dependence is incorrect.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate inverted the de Broglie relationship.

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Exact Duane-Hunt relation: minimum X-ray wavelength is inversely proportional to accelerating voltage.

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Why this is airtight: None. Candidate correctly applied conservation of energy for photon emission.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

This is the de Broglie wavelength of the electron, NOT the X-ray photon wavelength!

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Student Fallacy (Why candidates pick this trap): Over 40% of aspirants pick 1/√V because they confuse the de Broglie wavelength of matter waves (λ = h/p = h/√(2meV) ∝ 1/√V) with the electromagnetic photon wavelength (λ = hc/eV ∝ 1/V).

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NTA Trap Alert: The Classic de Broglie Wave (1/√V) vs X-ray Photon (1/V) Confusion

NTA intentionally includes 1/√V (Option 4) as a major trap. Matter waves (electron wavelength) scale with 1/√V, but electromagnetic radiation photons (X-rays) scale with 1/V.

🛡️ How to avoid the -1 mark: Rule: Electron matter wave λ ∝ 1/√V. X-ray photon λ_min ∝ 1/V.

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Dual Nature of Radiation and Matter Standard Benchmark

Core Scientific Principle Tested:

"Cutoff X-ray wavelength represents the maximum single-photon quantum energy: hc/λ_min = eV."

Syllabus Focus: Continuous X-rays and Duane-Hunt Law

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 16 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Duane-Hunt Inverse Voltage Law (12400 / V Å)

Step-by-Step Rigorous Workflow & Mathematical Proof

Kinetic Energy of Accelerated Electron

Maximum Photon Energy and Cutoff Wavelength

Proportionality Derivation

360° Option Elimination Engine Key Feature

NTA Trap Alert: The Classic de Broglie Wave (1/√V) vs X-ray Photon (1/V) Confusion

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Dual Nature of Radiation and Matter

Photocurrent and Stopping Potential Variation with Linearly Decreasing Light Power

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