Q.6 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 6 Solution

Topic: Atoms · Official NTA Booklet Code G5

Question

In hydrogen spectrum, the shortest wavelength in the Balmer series is λ. The shortest wavelength in the Bracket series is:

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Verified Against NTA Final Answer Key

Option (3) : 4 λ

📚 Atoms Easy

📋 Given Parameters & Problem Setup

Shortest wavelength in Balmer series λ

Target Series Brackett series

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The 30-Second Exam Hall Shortcut: ⚡ n₁² Series Limit Direct Scaling Shortcut

⏱️ Save ~40 seconds

For shortest wavelength (n₂ = ∞), λ ∝ n₁²! Balmer has n₁=2 (2²=4), Brackett has n₁=4 (4²=16); 16/4 = 4 → λ_Brackett = 4λ in 5 seconds!

1 Shortest wavelength corresponds to transition from infinity: 1/λ = R (1/n₁² - 0) = R / n₁².

2 Therefore, λ_min is directly proportional to n₁²: λ ∝ n₁².

3 For Balmer series, n₁ = 2 → λ ∝ 2² = 4.

4 For Brackett series, n₁ = 4 → λ_Brackett ∝ 4² = 16.

5 Ratio: λ_Brackett / λ_Balmer = 16 / 4 = 4 → λ_Brackett = 4λ. Instant Option (3)!

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Why You Can 100% Trust This Shortcut: Fundamental Atomic Physics · Bohr Rydberg Formula (Series limit condition: 1/λ_min = R_H / n₁²).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Rydberg Formula for Hydrogen Transitions

The wavelength λ of radiation emitted during an electronic transition from state n₂ to state n₁ in hydrogen is given by the Rydberg formula:

\frac{1}{\lambda} = R \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)

Step 2

Shortest Wavelength (Series Limit) Condition

The shortest wavelength corresponds to the maximum energy transition, which occurs from n₂ = ∞ to the ground level of that series (n₁):

\frac{1}{\lambda_{\text{min}}} = R \left(\frac{1}{n_1^2} - \frac{1}{\infty}\right) = \frac{R}{n_1^2} \implies \lambda_{\text{min}} = \frac{n_1^2}{R}

Step 3

Application to Balmer and Brackett Series

For the Balmer series, n₁ = 2. For the Brackett series, n₁ = 4:

\lambda_{\text{Balmer}} = \frac{2^2}{R} = \frac{4}{R} = \lambda \implies \frac{1}{R} = \frac{\lambda}{4}

Step 4

Evaluation of Brackett Series Limit

Substitute 1/R into the expression for Brackett series limit:

\lambda_{\text{Brackett}} = \frac{4^2}{R} = \frac{16}{R} = 16 \times \left(\frac{\lambda}{4}\right) = 4\lambda

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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:

Overestimates by a factor of 4.

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Student Fallacy (Why candidates pick this trap): Candidate took n₁² = 16 but forgot that the original Balmer wavelength already contains a factor of 4 (i.e. didn't divide by 4).

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Linearly scales with n₁ instead of quadratic scaling.

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Student Fallacy (Why candidates pick this trap): Candidate scaled λ linearly with n₁ ratio (4/2 = 2) instead of n₁².

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Exact ratio derived from quadratic series limit scaling (16 / 4 = 4).

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Why this is airtight: None. Candidate correctly applied the series limit relationship.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Corresponds to Paschen series limit relative to a different reference.

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Student Fallacy (Why candidates pick this trap): Candidate confused the Brackett series (n₁ = 4) with the Paschen series (n₁ = 3, where 3² = 9).

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NTA Trap Alert: Linear vs Quadratic Quantum Number Scaling

Aspirants frequently forget that energy levels follow 1/n² while wavelengths scale with n₁² for series limits. Scaling linearly (4/2 = 2) leads directly to the trap Option (2).

🛡️ How to avoid the -1 mark: Memorize: Series limit shortest wavelength λ_min = n₁² / R.

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Atoms Standard Benchmark

Core Scientific Principle Tested:

"Lyman (1), Balmer (2), Paschen (3), Brackett (4), Pfund (5). For shortest wavelength, λ_min ∝ n₁²."

Syllabus Focus: Bohr Model and Spectral Series of Hydrogen Atom

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 6 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ n₁² Series Limit Direct Scaling Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Rydberg Formula for Hydrogen Transitions

Shortest Wavelength (Series Limit) Condition

Application to Balmer and Brackett Series

Evaluation of Brackett Series Limit

360° Option Elimination Engine Key Feature

NTA Trap Alert: Linear vs Quadratic Quantum Number Scaling

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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