Q.175 Physics ⭐ 360° Option Elimination Active

NEET 2020 Physics Question 175 Solution

Topic: Dual Nature of Radiation and Matter · Official NTA Booklet Code E1

Question

An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227×10⁻² nm, the potential difference is:

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Verified Against NTA Final Answer Key

Option (4) : 10^4 V

📚 Dual Nature of Radiation and Matter Medium

📋 Given Parameters & Problem Setup

de Broglie Wavelength lambda = 1.227 × 10^-2 nm

Standard Formula for Electron lambda = 1.227 / sqrt(V) nm

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The 30-Second Exam Hall Shortcut: ⚡ "lambda = 1.227 / sqrt(V) nm => 1.227 × 10^-2 = 1.227 / sqrt(V) => sqrt(V) = 100 => V = 100^2 = 10000 V = 10^4 V!"

⏱️ 20 seconds

For an electron accelerated through potential difference V, de Broglie wavelength is lambda = 1.227 / sqrt(V) nm. Equating to 1.227 × 10^-2 nm gives sqrt(V) = 1 / 10^-2 = 100 => V = 100^2 = 10000 V = 10^4 V. Don't forget to square 100! Mark Option (4) in 5 seconds.

1 Formula:

\lambda = \frac{1.227}{\sqrt{V}}\text{ nm}

2 Substitute given wavelength:

1.227 \times 10^{-2}\text{ nm} = \frac{1.227}{\sqrt{V}}\text{ nm}

3 Cancel 1.227:

\sqrt{V} = \frac{1}{10^{-2}} = 100

4 Square to find potential:

V = (100)^2 = 10^4\text{ V}

5 Select Option (4).

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Why You Can 100% Trust This Shortcut: NCERT Physics · Dual Nature of Radiation and Matter (de Broglie Wavelength of an Electron)

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for de Broglie Wavelength of Accelerated Electron

An electron of mass $m$ and charge $e$ accelerated from rest through potential difference $V$ acquires kinetic energy $K = eV$ . Its de Broglie wavelength is: $\lambda = \frac{h}{p} = \frac{h}{\sqrt{2m e V}}$ .

Step 2

Substitute Universal Constants

Substituting $h = 6.626 \times 10^{-34}\text{ J s}$ , $m = 9.1 \times 10^{-31}\text{ kg}$ , and $e = 1.6 \times 10^{-19}\text{ C}$ gives the standard compact formula: $\lambda = \frac{1.227}{\sqrt{V}}\text{ nm} = \frac{12.27}{\sqrt{V}}\text{ \AA}$ .

Step 3

Equate and Solve for Potential V

Given $\lambda = 1.227 \times 10^{-2}\text{ nm}$ : $1.227 \times 10^{-2} = \frac{1.227}{\sqrt{V}}$ Divide both sides by $1.227$ : $10^{-2} = \frac{1}{\sqrt{V}} \implies \sqrt{V} = 10^2 = 100$ . Squaring both sides: $V = 100^2 = 10000\text{ V} = 10^4\text{ V}$ .

Step 4

Conclude and Verify

Matches Option 4.

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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; for V = 10 V, lambda ≈ 0.388 nm.

⚠️

Student Fallacy (Why candidates pick this trap): Random power-of-ten mismatch.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; forgets to square sqrt(V) = 100, answering 100 V instead of 10000 V.

⚠️

Student Fallacy (Why candidates pick this trap): Classic error of forgetting to square sqrt(V).

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; corresponds to sqrt(V) ≈ 31.6 V.

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic miscalculation.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value; sqrt(V) = 100 => V = 100^2 = 10^4 V.

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Why this is airtight: None; remembers to square the square-root term.

⚠️

NTA Trap Alert: Squaring the Square Root

Students frequently solve for sqrt(V) = 100 and immediately mark 100 V (10^2 V, Option B). The potential is V, so you MUST square it: (100)^2 = 10^4 V.

🛡️ How to avoid the -1 mark: Always write: V = (sqrt(V))^2 = 100^2 = 10^4 V.

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Core NEET Syllabus Standard

Physics · Dual Nature of Radiation and Matter Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: Accelerating Potential for an Electron from de Broglie Wavelength

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Physics Question 175 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "lambda = 1.227 / sqrt(V) nm => 1.227 × 10^-2 = 1.227 / sqrt(V) => sqrt(V) = 100 => V = 100^2 = 10000 V = 10^4 V!"

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for de Broglie Wavelength of Accelerated Electron

Substitute Universal Constants

Equate and Solve for Potential V

Conclude and Verify

360° Option Elimination Engine Key Feature

NTA Trap Alert: Squaring the Square Root

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Dual Nature of Radiation and Matter

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