JEE Main 2023 · 31 January · morning · Single correct · +4 / −1
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The beam of electrons show wave nature and exhibit interference and diffraction.
Reason R : Davisson Germer Experimentally verified the wave nature of electrons.
In the light of the above statements, choose the most appropriate answer from the options given below :
- (a) A is not correct but R is correct.
- (b) Both A and R are correct and R is the correct explanation of A
- (c) Both A and R are correct but R is Not the correct explanation of A
- (d) A is correct but R is not correct
Answer and solution
Answer (b) Both A and R are correct and R is the correct explanation of A
Solution
Physics sir · 4 steps
Check each statement on its own first, then ask whether R is the evidence that makes A true.
- Assertion A. A moving electron has a de Broglie wavelength λ = h/p. A beam of electrons therefore behaves like a wave and shows diffraction and interference. That is the principle behind electron microscopes and electron diffraction from thin crystals. A is correct.
- Reason R. In 1927 Davisson and Germer fired 54 eV electrons at a nickel crystal and found a sharp intensity peak at a scattering angle of 50°. That peak is a diffraction maximum, the same thing X-rays give. R is correct.
λ = h/√2meV = 12.27/√54 Å ≈ 1.67 Å
- Link between them. The wavelength measured from the diffraction peak, about 1.65 Å, matched the de Broglie value above. This experiment is the proof that electron beams diffract, so R is exactly why we accept A.
- So. Both statements are correct and R correctly explains A, which is option (b).
The idea to keep. Davisson-Germer is the experiment that proved matter waves are real: electrons diffracted from a nickel crystal at the wavelength de Broglie predicted. Whenever electron diffraction comes up, that is its evidence.
Answer from the NTA final answer key. Solution by PrepWiser.