Q.54 Chemistry ⭐ 360° Option Elimination Active

NEET 2021 Chemistry Question 54 Solution

Topic: Structure of Atom · Official NTA Booklet Code M1

Question

A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is: [speed of light, c = 3.0×10⁸ m s⁻¹]

✓

Verified Against NTA Final Answer Key

Option (1) : 219.3 m

📚 Structure of Atom Easy

📋 Given Parameters & Problem Setup

Broadcasting Frequency (ν) 1,368 kHz = 1,368 × 10^3 Hz

Speed of Light (c) 3.0 × 10^8 m/s

⚡

The 30-Second Exam Hall Shortcut: ⚡ Fast Wave Formula: λ = c / ν

⏱️ Save ~20 seconds

$\lambda = \frac{3.0 \times 10^8}{1368 \times 10^3} = \frac{300,000}{1368} = 219.298\text{ m} \approx 219.3\text{ m}$ ! Direct 10-second division matching Option (1)!

1 Convert frequency to SI base units:

\nu = 1368\text{ kHz} = 1.368 \times 10^6\text{ s}^{-1}

2 Wave equation:

c = \nu \lambda \implies \lambda = \frac{c}{\nu}

3 Substitute:

\lambda = \frac{3.0 \times 10^8\text{ m/s}}{1368 \times 10^3\text{ s}^{-1}} = \frac{3000}{13.68} = 219.298\text{ m}

4 Round to 4 significant figures:

219.3\text{ m}

5 Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical wave mechanics velocity-frequency-wavelength relation (

c = \nu \lambda

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Stating the Fundamental Wave Equation

For any electromagnetic radiation propagating in vacuum or air, the speed of light $c$ is related to frequency $\nu$ and wavelength $\lambda$ by:

c = \nu \cdot \lambda \implies \lambda = \frac{c}{\nu}

Step 2

Converting Frequency to Standard SI Units

The given frequency is in kilohertz ( $1\text{ kHz} = 10^3\text{ Hz} = 10^3\text{ s}^{-1}$ ):

\nu = 1368\text{ kHz} = 1368 \times 10^3\text{ Hz} = 1.368 \times 10^6\text{ s}^{-1}

Step 3

Computing the Wavelength

Substitute $c = 3.0 \times 10^8\text{ m/s}$ and $\nu = 1.368 \times 10^6\text{ s}^{-1}$ :

\lambda = \frac{3.0 \times 10^8\text{ m/s}}{1.368 \times 10^6\text{ s}^{-1}} = \frac{300}{1.368}\text{ m} = 219.298\text{ m} \approx 219.3\text{ m}

⭐

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

✓ 100% Correct

Verdict & Scientific Reason:

Exact wavelength: $3.0 \times 10^8 / (1368 \times 10^3) = 219.298\text{ m} \approx 219.3\text{ m}$ .

💡

Why this is airtight: None; precise arithmetic calculation.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Truncates without rounding up ( $219.298$ rounds up to $219.3$ , not $219.2$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Truncation error rather than proper mathematical rounding.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Off by a factor of 10 from mishandling powers of ten ( $10^8 / 10^3$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Order of magnitude exponent subtraction error.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Gross unit mismatch (centimeters instead of meters).

⚠️

Student Fallacy (Why candidates pick this trap): Unit confusion.

⚠️

NTA Trap Alert: Rounding vs. Truncation Trap (Option 1 vs. Option 2)

The raw division gives $219.298\text{ m}$ . Candidates who truncate to 4 digits get $219.2\text{ m}$ (Option 2). Applying correct significant figure rounding rules to the next digit (9) requires rounding UP to $219.3\text{ m}$ (Option 1).

🛡️ How to avoid the -1 mark: Since

0.298 > 0.25

, round UP to

0.3

219.3\text{ m}

📖

Core NEET Syllabus Standard

NCERT Chemistry · Structure of Atom Standard Benchmark

Core Scientific Principle Tested:

"The wavelength of electromagnetic radiation is $\lambda = c / \nu$ ."

Syllabus Focus: Wave Nature of Electromagnetic Radiation

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Chemistry Question 54 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Fast Wave Formula: λ = c / ν

Step-by-Step Rigorous Workflow & Mathematical Proof

Stating the Fundamental Wave Equation

Converting Frequency to Standard SI Units

Computing the Wavelength

360° Option Elimination Engine Key Feature

NTA Trap Alert: Rounding vs. Truncation Trap (Option 1 vs. Option 2)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Structure of Atom

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