Q.34 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 34 Solution

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

Question

De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm)

✓

Verified Against NTA Final Answer Key

Option (2) : 0.67 nm

📚 Dual Nature of Radiation and Matter Easy

📋 Given Parameters & Problem Setup

Principal Quantum Number (n) 2

Bohr Radius (a₀) 0.052 nm

Target Variable de Broglie wavelength λ of electron

⚡

The 30-Second Exam Hall Shortcut: ⚡ Bohr-de Broglie Standing Wave Shortcut

⏱️ Save ~40 seconds

2π r_n = n λ ⟹ For n = 2: 2π r₂ = 2λ ⟹ λ = π r₂ = π (a₀ n²) = π (0.052 × 4) = 3.14 × 0.208 ≈ 0.67 nm!

1 Recall de Broglie’s standing wave condition for stationary Bohr orbits: Circumference = n wavelengths ⟹ 2π r_n = n λ.

2 For the n = 2 state: 2π r₂ = 2 λ ⟹ λ = π r₂.

3 Calculate radius of n = 2 orbit: r₂ = a₀ · n² = 0.052 nm × 2² = 0.052 × 4 = 0.208 nm.

4 Calculate wavelength: λ = π × 0.208 nm ≈ 3.1416 × 0.208 ≈ 0.653 nm ≈ 0.67 nm (using standard a₀ = 0.0529 nm gives exactly 0.665 nm ≈ 0.67 nm).

5 Match Option (2) in under 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: de Broglie’s Standing Wave Quantization (NCERT Physics · Atoms: 2πr = nλ).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Bohr-de Broglie Condition for Stationary Orbits

Louis de Broglie explained Bohr’s angular momentum quantization by proposing that an electron in an orbit behaves as a standing matter wave. Constructive interference requires the orbital circumference to contain an integral number of de Broglie wavelengths:

2\pi r_n = n \lambda \implies \lambda = \frac{2\pi r_n}{n}

• For n = 2: λ = 2π r₂ / 2 = π r₂.

Step 2

Calculate Radius of n = 2 Orbit

The radius of the n-th Bohr orbit scales with the square of the principal quantum number:

r_n = a_0 n^2 \implies r_2 = 0.052\text{ nm} \times (2)^2 = 0.052 \times 4 = 0.208\text{ nm}

• r₂ = 0.208 nm (or 0.212 nm with standard a₀ = 0.0529 nm).

Step 3

Calculate de Broglie Wavelength

Substitute r₂ into the wavelength relation:

\lambda = \pi r_2 = 3.1416 \times 0.208\text{ nm} \approx 0.653\text{ nm} \approx 0.67\text{ nm}

• Matches Option (2) 0.67 nm.

⭐

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. Off by a factor of 10 (decimal place error).

⚠️

Student Fallacy (Why candidates pick this trap): Order of magnitude calculation slip.

2 B

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. λ = π r₂ = π (4 × 0.052 nm) ≈ 0.67 nm.

💡

Why this is airtight: None; textbook matter wave standing wave relation.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Exceeds the circumference of the orbit.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by extraneous factors.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to n = 4 calculation error.

⚠️

Student Fallacy (Why candidates pick this trap): Using n = 4 or incorrect orbit radius.

⚠️

NTA Trap Alert: Calculating via Velocity Instead of 2πr = nλ

Students often try to compute electron velocity v = e² / (2ε₀ n h), then momentum p = mv, then λ = h/p. This lengthy method introduces high chances of numerical arithmetic mistakes. Using 2πr = nλ gives the answer in one line!

🛡️ How to avoid the -1 mark: Whenever de Broglie wavelength in a Bohr orbit is asked, always use 2πr = nλ.

📖

Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"Circumference contains integer wavelengths: 2π r_n = n λ."

Syllabus Focus: de Broglie Wavelength & Bohr Orbitals

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

n = 2 ⟹ λ = π r₂ = π (4 × 0.052 nm) ≈ 0.67 nm!

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 180-minute timed NTA simulator.

Launch NEET 2025 CBT Test →

← Previous (Q.33) All Physics Questions Grid Next (Q.35) →

🔗 Related Questions — Dual Nature of Radiation and Matter

All 15 Dual Nature of Radiation and Matter PYQs →

NEET 2026 Q8

Photocurrent and Stopping Potential Variation with Linearly Decreasing Light Power

View Solution →

NEET 2026 Q18

Spotted a mistake in this solution? Report an error ([email protected])

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2025 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

NEET 2025 Physics Question 34 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Bohr-de Broglie Standing Wave Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Bohr-de Broglie Condition for Stationary Orbits

Calculate Radius of n = 2 Orbit

Calculate de Broglie Wavelength

360° Option Elimination Engine Key Feature

NTA Trap Alert: Calculating via Velocity Instead of 2πr = nλ

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

Threshold Wavelength Condition and Stopping Potential Ordering

Ratio of Linear Momentum of Electron to Photon for Equal Kinetic Energies

Characteristics and Properties of Photons

Solve 4 NEET Questions a Day — One per Subject