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.

Step 1 (Governing Principle): [0.25 Mark]

According to the de Broglie hypothesis, every moving particle (including electrons) is associated with a wave nature. The wavelength ($\lambda$) associated with a particle of momentum ($p$) is given by:

Where $h$ is Planck's constant, $m$ is the mass, and $v$ is the velocity of the electron.

Step 2 (Logical Deduction): [0.50 Mark]

• Assertion (A): Diffraction is a characteristic property of waves. When electrons are accelerated, they possess a de Broglie wavelength. If this wavelength is comparable to the dimensions of the slit (or the inter-atomic spacing in a crystal), the electrons undergo diffraction, similar to light waves. This was experimentally verified by the Davisson-Germer experiment.
• Reason (R): The wave-particle duality of matter states that electrons exhibit both particle-like properties (e.g., collisions, charge) and wave-like properties (e.g., interference, diffraction). The diffraction pattern is direct evidence of the wave nature of electrons.

Step 3 (Final Concluded Answer): [0.25 Mark]

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

💡 EL10 Concept Insight: Think of an electron like a tiny, super-fast marble that can also act like a ripple in a pond. Because it acts like a ripple, when it hits a tiny gap, it spreads out and creates a pattern of light and dark spots (diffraction) just like water waves do when they pass through a narrow opening!