Question

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.

• 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.

Hint:

Whenever diffraction or interference is observed for a particle, it is direct evidence of its wave nature and hence confirms de Broglie's hypothesis.

Answer 1

The Correct Option is A

Concept: According to de Broglie's hypothesis, every moving particle has an associated wavelength given by \[ \lambda=\frac{h}{p}=\frac{h}{mv}. \] Thus, electrons exhibit wave properties in addition to particle properties. This is known as the wave-particle duality of matter. Diffraction is a phenomenon associated with waves. Therefore, if electrons produce diffraction patterns, it directly confirms their wave nature.

Step 1: Examine the Assertion (A).
When accelerated electrons are passed through a narrow slit or a crystal, they undergo diffraction and produce a diffraction pattern. Hence, Assertion (A) is true.

Step 2: Examine the Reason (R).
Electrons possess both particle and wave characteristics. This is experimentally verified by electron diffraction experiments such as the Davisson-Germer experiment. Hence, Reason (R) is true.

Step 3: Determine whether the reason explains the assertion.
The diffraction pattern is observed precisely because electrons behave as waves. Therefore, the Reason correctly explains the Assertion. Hence, \[ \boxed{\text{Both A and R are true and R is the correct explanation of A.}} \]