Question 141 markSection A

Assertion (A): If accelerated electrons are passed through a narrow slit, a diffraction pattern is observed.

Reason (R): Electrons behave as both particles and waves.

Dual Nature of Radiation and Matter
Matter waves and electron diffraction

Options

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Both Assertion (A) and Reason (R) are false.

Official answer

Correct option: (A) — Both statements are true and R is the correct explanation of A.


Why A is true: Accelerated electrons have a de Broglie wavelength λ=h/p\lambda = h/p comparable to atomic/slit dimensions, so they diffract — confirmed by the Davisson–Germer experiment and G.P. Thomson's electron diffraction.


Why R is the correct explanation: Diffraction is a purely wave phenomenon. Electrons can diffract only because they possess a wave nature alongside their particle nature — exactly what R states.

Answer keywords:de Broglie wavelengthelectron diffractionwave-particle dualityDavisson-Germermatter waveslambda = h/pwave nature of electron

Marking scheme

  1. 1.1 mark: correct option (A).
  2. 2.Both statements true and causal link recognised.

Hint

Diffraction is a wave effect; recall Davisson–Germer confirming λ=h/p\lambda = h/p for electrons.

Quick oral answer

Both true and R explains A: electrons have a de Broglie wavelength lambda equals h over p, so they diffract at a narrow slit; diffraction is a wave phenomenon, which is exactly the wave nature R refers to.

Common mistakes

  1. 1.Selecting (B) — R is not merely correlated but is the actual cause of the diffraction, so it is the correct explanation.
  2. 2.Thinking diffraction proves electrons are only waves; they still behave as particles too (duality).
  3. 3.Assuming ordinary macroscopic objects would also visibly diffract — their λ is far too small.

Analysis and explanation

Concept:

de Broglie proposed that every moving particle has an associated wavelength λ=h/p\lambda = h/p. For electrons this wavelength is small but not negligible.


Assertion analysis:

  • Electrons accelerated through a potential V gain momentum p=2meVp = \sqrt{2meV}; their λ works out to ~ a few tenths of a nanometre.
  • Passing them through a slit or crystal comparable to λ produces a diffraction pattern.

Reason analysis:

  • Wave–particle duality means electrons show particle behaviour (charge, mass, discrete detection) and wave behaviour (diffraction, interference).
  • Since diffraction is inherently a wave effect, the wave nature is precisely why the pattern forms — so R correctly explains A.

Exam trap:

Do not pick (B). Here the Reason is not just a true statement standing alone; it is the direct cause of the assertion.


Real-world:

Electron diffraction underpins the electron microscope and LEED (low-energy electron diffraction) used to study crystal surfaces.

Interesting facts

The Davisson–Germer experiment (1927) accidentally revealed electron diffraction after a vacuum accident recrystallised their nickel target.

G.P. Thomson won the 1937 Nobel Prize for showing electrons diffract — his father J.J. Thomson had won it for showing the electron is a particle.

A 100 eV electron has a de Broglie wavelength near 0.12 nm, similar to X-rays, making electron diffraction ideal for probing crystals.

Question details

Q14 of 39 questions

Board
CBSE
Class
Class 12
Subject
Physics
Year
2026
Section
Section A
Marks
1
Chapter
Dual Nature of Radiation and Matter
Topic
Matter waves and electron diffraction
Bloom's level
understand
Syllabus topic
Unit VII: Dual Nature of Radiation and Matter — de Broglie waves; wave nature of electrons
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Why do electrons produce a diffraction pattern?

Accelerated electrons have a de Broglie wavelength λ=h/p\lambda = h/p comparable to slit or crystal spacings, so they diffract just like light waves, forming maxima and minima.

Why is R the correct explanation and not just a related fact?

Diffraction is a wave phenomenon; electrons can diffract only because of their wave nature, so the duality stated in R is the direct cause of the assertion.

Which experiment confirmed this?

The Davisson–Germer experiment (1927) and G.P. Thomson's work confirmed that electrons diffract, verifying de Broglie's matter-wave hypothesis.