Q.37 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 37 Solution

Topic: Dual Nature of Radiation and Matter · Official NTA Booklet Code 45

Question

A photon and an electron (mass m) have the same energy E. The ratio (λ_photon/λ_electron) of their de Broglie wavelengths is: (c is the speed of light)

✓

Verified Against NTA Final Answer Key

Option (3) : c \sqrt{\frac{2m}{E}}

📚 Dual Nature of Radiation and Matter Easy

📋 Given Parameters & Problem Setup

Equal Energy for Both Particles E

Photon Properties Speed c, energy E = h c / λ_ph

Electron Properties Mass m, kinetic energy E = p² / (2m)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Photon-Electron Ratio Rule

⏱️ Save ~30 seconds

λ_ph = hc / E, λ_e = h / √(2mE) ⟹ λ_ph / λ_e = (hc/E) / (h/√(2mE)) = c √(2mE) / E = c √(2m/E)!

1 Write wavelength of photon in terms of energy E: E = h c / λ_ph ⟹ λ_ph = h c / E.

2 Write de Broglie wavelength of electron in terms of kinetic energy E: λ_e = h / p = h / √(2 m E).

3 Take the ratio: λ_ph / λ_e = (h c / E) ÷ (h / √(2 m E)).

4 Simplify: (c / E) × √(2 m E) = c × √(2 m E / E²) = c √(2 m / E).

5 Select Option (3) in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: de Broglie Hypothesis (NCERT Physics · Dual Nature of Radiation and Matter: λ = h/p).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Express de Broglie Wavelength of the Photon

For electromagnetic radiation (photons), energy is related to wavelength by the Planck-Einstein relation:

E = h \nu = \frac{h c}{\lambda_{photon}} \implies \lambda_{photon} = \frac{h c}{E}

• c is the speed of light in vacuum.

Step 2

Express de Broglie Wavelength of the Electron

For a massive non-relativistic particle of mass m and kinetic energy E, momentum is p = √(2 m E):

\lambda_{electron} = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}

• This is de Broglie’s fundamental relation for matter waves.

Step 3

Calculate the Ratio of Wavelengths

Divide the photon wavelength by the electron wavelength:

\frac{\lambda_{photon}}{\lambda_{electron}} = \frac{\frac{h c}{E}}{\frac{h}{\sqrt{2 m E}}} = \frac{h c}{E} \times \frac{\sqrt{2 m E}}{h} = c \frac{\sqrt{2 m E}}{E} = c \sqrt{\frac{2 m}{E}}

• Matches Option (3) 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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Missing the factor of c and inverts the ratio inside the square root.

⚠️

Student Fallacy (Why candidates pick this trap): Dimensionally inconsistent with a dimensionless ratio.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Leaves E in the numerator inside the radical instead of denominator.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying instead of dividing by E.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. Dimensionally and physically exact: λ_ph / λ_e = c √(2m/E).

💡

Why this is airtight: None; flawless algebraic derivation.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Inverted ratio (λ_e / λ_ph).

⚠️

Student Fallacy (Why candidates pick this trap): Calculating the reciprocal ratio λ_electron / λ_photon.

⚠️

NTA Trap Alert: Inverted Ratio Trap (λ_e / λ_ph)

Candidates often calculate the ratio upside down, leading them to select Option (4) (1/c √(E/2m)). Always double-check which quantity is in the numerator!

🛡️ How to avoid the -1 mark: Dimensional check: Since photon has longer wavelength than non-relativistic electron of same energy, the ratio must be >> 1, requiring c in the numerator.

📖

Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"λ_ph = hc / E and λ_e = h / √(2mE)."

Syllabus Focus: Wave-Particle Duality and de Broglie Wavelength

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Photon has c on top: λ_ph / λ_e = c √(2m / E)!

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NEET 2025 Physics Question 37 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Photon-Electron Ratio Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Express de Broglie Wavelength of the Photon

Express de Broglie Wavelength of the Electron

Calculate the Ratio of Wavelengths

360° Option Elimination Engine Key Feature

NTA Trap Alert: Inverted Ratio Trap (λ_e / λ_ph)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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