Q.46 Chemistry ⭐ 360° Option Elimination Active

NEET 2025 Chemistry Question 46 Solution

Topic: Structure of Atom · Official NTA Booklet Code 45

Question

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is

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Verified Against NTA Final Answer Key

Option (4) : \frac{1}{4}

📚 Structure of Atom Easy

📋 Given Parameters & Problem Setup

Transition 1 n = 2 → n = 3

Transition 2 n = 4 → n = 6

Target Ratio λ₁ / λ₂ (wavelength of light absorbed in transition 1 to transition 2)

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The 30-Second Exam Hall Shortcut: ⚡ Scaled Orbit Rydberg Shortcut

⏱️ Save ~40 seconds

Notice transition 2 has double the quantum numbers of transition 1: (4 = 2×2, 6 = 2×3). Since 1/λ ∝ 1/n², doubling all n values scales 1/λ by 1/2² = 1/4 ⟹ λ₂ = 4 λ₁ ⟹ λ₁ / λ₂ = 1/4!

1 Notice quantum scaling: n₁ = 2, n₂ = 3 for transition 1; n₁' = 4 = 2(2), n₂' = 6 = 2(3) for transition 2.

2 Wavenumber formula: 1/λ = R_H (1/n₁² - 1/n₂²).

3 When both quantum numbers are multiplied by a factor of 2: 1/λ₂ = R_H [1/(2×2)² - 1/(2×3)²] = (1/4) × R_H (1/2² - 1/3²) = (1/4) (1/λ₁).

4 Therefore: λ₁ / λ₂ = 1/4.

5 Select Option (4) in under 10 seconds without calculating full fractions!

🛡️

Why You Can 100% Trust This Shortcut: Rydberg Formula for Hydrogen Atom Transitions (NCERT Chemistry · Structure of Atom: 1/λ = R_H Z² (1/n₁² - 1/n₂²)).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Apply Rydberg Formula to Transition 1 (n = 2 → n = 3)

According to the Rydberg formula, the reciprocal of the absorbed wavelength for hydrogen is:

\frac{1}{\lambda_1} = R_H \left(\frac{1}{2^2} - \frac{1}{3^2}\right) = R_H \left(\frac{1}{4} - \frac{1}{9}\right) = R_H \left(\frac{9 - 4}{36}\right) = \frac{5}{36} R_H

• Inverting gives: λ₁ = 36 / (5 R_H).

Step 2

Apply Rydberg Formula to Transition 2 (n = 4 → n = 6)

For the transition between n = 4 and n = 6:

\frac{1}{\lambda_2} = R_H \left(\frac{1}{4^2} - \frac{1}{6^2}\right) = R_H \left(\frac{1}{16} - \frac{1}{36}\right) = R_H \left(\frac{9 - 4}{144}\right) = \frac{5}{144} R_H

• Inverting gives: λ₂ = 144 / (5 R_H).

Step 3

Calculate the Wavelength Ratio

Divide the two wavelengths:

\frac{\lambda_1}{\lambda_2} = \frac{\frac{36}{5 R_H}}{\frac{144}{5 R_H}} = \frac{36}{144} = \frac{1}{4}

• Matches Option (4) exactly.

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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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Forgets common factor 5/R_H or squares denominator.

⚠️

Student Fallacy (Why candidates pick this trap): Squaring the ratio 1/6.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Squaring the 1/4 factor.

⚠️

Student Fallacy (Why candidates pick this trap): Squaring the scaling factor (1/4)² = 1/16.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Ratio of 1/n² terms.

⚠️

Student Fallacy (Why candidates pick this trap): Dividing 4 by 36.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. λ₁ / λ₂ = 36 / 144 = 1/4.

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Why this is airtight: None; flawless Rydberg calculation.

⚠️

NTA Trap Alert: Inverting Wavenumber Ratio vs Wavelength Ratio

Calculating (1/λ₁) / (1/λ₂) = 144/36 = 4, then forgetting that λ₁/λ₂ is the reciprocal 1/4.

🛡️ How to avoid the -1 mark: Remember: 1/λ is wavenumber; wavelength λ is its inverse!

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Core NEET Syllabus Standard

NEET Chemistry Core Syllabus · Structure of Atom Standard Benchmark

Core Scientific Principle Tested:

"1/λ = R_H (1/n₁² - 1/n₂²)."

Syllabus Focus: Bohr’s Model & Rydberg Formula for Hydrogen Spectrum

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Doubled levels ⟹ 1/λ drops by 2² = 4 ⟹ λ quadruples ⟹ λ₁ / λ₂ = 1/4!

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All Chemistry Questions Grid Next (Q.47) →

Mathematical Relation Between Number of Magnetic Orbitals (n_m) and Azimuthal Quantum Number (l)

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NEET 2025 Chemistry Question 46 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Scaled Orbit Rydberg Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Apply Rydberg Formula to Transition 1 (n = 2 → n = 3)

Apply Rydberg Formula to Transition 2 (n = 4 → n = 6)

Calculate the Wavelength Ratio

360° Option Elimination Engine Key Feature

NTA Trap Alert: Inverting Wavenumber Ratio vs Wavelength Ratio

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Structure of Atom

Radial Wavefunctions and Identification of Radial Nodes

Physical Significance of the Four Quantum Numbers

Bohr Energy Levels in Hydrogen-like Mononuclear Ions

Mathematical Relation Between Number of Magnetic Orbitals (n_m) and Azimuthal Quantum Number (l)

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