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 ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 200-minute timed NTA simulator.

Launch NEET 2021 CBT Test →

← Previous (Q.53) All Chemistry Questions Grid Next (Q.55) →

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

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2021 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 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

Radial Wavefunctions and Identification of Radial Nodes

Ratio of Wavelengths of Absorbed Light in Rydberg Transitions

Energy and Radius of First Bohr Orbit for He⁺ and Li²⁺

Physical Significance of the Four Quantum Numbers

Solve 4 NEET Questions a Day — One per Subject