PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2024: question 20

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section B, question 20, for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Consider a neutron (mass m) of kinetic energy E and a photon of the same energy. Let $λ_{n}$ and $λ_{p}$ be the de Broglie wavelength of neutron and the wavelength of photon respectively. Obtain an expression for $\frac{λ _{n}}{λ _{p}}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/1/1.

Hints

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

Hint 1

The photon's energy and wavelength are linked through $E = h c / λ$ .

Hint 2

For the neutron, express its momentum in terms of its kinetic energy, then use $λ = h / p$ .

Hint 3

Divide the two expressions and simplify the square root.

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.

For the photon, $E = \frac{h c}{λ _{p}}$ , so $λ_{p} = \frac{h c}{E}$ .
½ mark
For the neutron, $E = \frac{p ^{2}}{2 m}$ gives $p = 2 m E$ , so $λ_{n} = \frac{h}{p} = \frac{h}{2 m E}$ .
½ mark
Ratio: $\frac{λ _{n}}{λ _{p}} = \frac{h}{2 m E} \times \frac{E}{h c}$ .
½ mark
$\frac{λ _{n}}{λ _{p}} = \frac{E}{2 m c ^{2}}$
½ mark

Answer: $\frac{λ _{n}}{λ _{p}} = \frac{E}{2 m c ^{2}}$

Where the marks are

Writes $λ_{p} = h c / E$ (½ mark)
Writes $λ_{n} = h / 2 m E$ (½ mark)
Forms the ratio (½ mark)
Simplifies to $E /2 m c^{2}$ (½ mark)

Revise the chapter

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

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 paper2024 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2024: question 20

Hints

Step-by-step solution

Revise the chapter

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