Plot a graph showing variation of de-Broglie wavelength λ versus (1)/(√(V)), where V is accelerating potential for a particle of mass m and charge q. Obtain the slope of this graph.

PhysicsCBSE Class 12 · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2025-26: question 21(II)

From the official CBSE sample question paper for 2025-26, section B, question 21(II), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(II) · 2 marks · Very short answerDual Nature of Radiation and Matter

Plot a graph showing variation of de-Broglie wavelength λ versus $\frac{1}{V}$ , where V is accelerating potential for a particle of mass m and charge q. Obtain the slope of this graph.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Relate momentum to accelerating potential using $q V = p^{2} /2 m$ .

Hint 2

Write λ in the form $y = m x$ with $x = 1/ V$ .

Step-by-step solution

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Kinetic energy gained: $\frac{1}{2} m v^{2} = q V \Rightarrow p = 2 m q V$ , so $λ = \frac{h}{p} = \frac{h}{2 m q} \cdot \frac{1}{V}$ . The graph of $λ$ (y-axis) against $1/ V$ (x-axis) is a straight line passing through the origin.
1 mark
Comparing with $y = m x$ , slope $= \frac{h}{2 m q}$ .
1 mark

Answer: Straight line through origin; slope $= h / 2 m q$

Where the marks are

Derives $λ = h / 2 m q V$ and plots straight line through origin (1 mark)
Slope $h / 2 m q$ (1 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

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CBSE Class 12 Physics sample paper 2025-26: question 21(II)

Hints

Step-by-step solution

Revise the chapter

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