PhysicsCBSE Class 12 · Board exam 2023, set 55/5/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2023: question 20(a)

Set in the CBSE Class 12 board exam of 2023, paper 55/5/1, section B, question 20(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q20(a) · 2 marks · Very short answerDual Nature of Radiation and Matter

How will the De Broglie wavelength associated with an electron be affected when the (i) velocity of the electron decreases ? and (ii) accelerating potential is increased ? Justify your answer.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Start from $λ = h / p$ .

Hint 2

For an accelerated electron, the kinetic energy $e V$ equals $p^{2} /2 m$ . Solve this for $p$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) The de Broglie wavelength is $λ = \frac{h}{m v}$ , so $λ \propto \frac{1}{v}$ .
½ mark
Therefore, when the velocity of the electron decreases, its de Broglie wavelength increases.
½ mark
(ii) For an electron accelerated through a potential $V$ , $e V = \frac{p ^{2}}{2 m}$ . This gives $λ = \frac{h}{2 m e V}$ , so $λ \propto \frac{1}{V}$ .
½ mark
Therefore, when the accelerating potential is increased, the de Broglie wavelength decreases.
½ mark

Answer: (i) λ increases (λ ∝ 1/v); (ii) λ decreases (λ ∝ 1/√V)

Where the marks are

States $λ = h / m v$ (½ mark)
Concludes λ increases when v decreases (½ mark)
States $λ = h / 2 m e V$ (½ mark)
Concludes λ decreases when V increases (½ mark)

Revise the chapter

Chapter: Dual Nature of Radiation and Matter (notes, formulas, where marks are lost and every past question)
Topic: de Broglie Wavelength

Practise this chapterBoard-style questions from Dual Nature of Radiation and Matter, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 55/5/1: every question, by section.

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CBSE Class 12 Physics 2023: question 20(a)

Hints

Step-by-step solution

Revise the chapter

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