Question

Match List I with List II:

List I	List II
A. $E = h\nu$  B. Diffraction and Interference  C. $\lambda = \frac{h}{p}$  D. Compton effect	I. de Broglie wavelength  II. Particle nature of light  III. Wave nature of light  IV. Energy of photon

• A. A-IV, B-I, C-II, D-III
• B. A-I, B-IV, C-III, D-II
• C. A-IV, B-III, C-II, D-I
• D. A-IV, B-III, C-I, D-II

Hint:

To remember the "nature" of light: Wave nature is proved by Interference/Diffraction/Polarization. Particle nature is proved by Photoelectric effect/Compton effect.

Answer 1

The Correct Option is D

Step 1: Understanding the Topic:
This question covers the "Dual Nature of Matter and Radiation." Modern physics establishes that light and matter can exhibit both wave-like and particle-like properties depending on the experiment being conducted. This matching exercise pairs specific formulas and phenomena with their underlying conceptual categories.
Step 2: Key Formulas and Approach:
The approach involves identifying the historical and mathematical milestones of quantum mechanics:
Planck's Equation: Relates frequency to energy.
de Broglie Hypothesis: Relates momentum to wavelength.
Classical Wave Theory: Explains spatial distribution of intensity.
Quantum Scattering: Explains momentum exchange.

Step 3: Detailed Explanation:

A $\rightarrow$ IV: $E = h\nu$ is the equation proposed by Max Planck and later used by Einstein to describe the energy of a single "packet" or photon of light. Thus, it represents the Energy of photon.
B $\rightarrow$ III: Diffraction and Interference involve the overlapping of waves and the addition of amplitudes. These cannot be explained by particle theory and serve as the primary evidence for the Wave nature of light.
C $\rightarrow$ I: $\lambda = h/p$ is the formula for the de Broglie wavelength. It suggests that a particle with momentum $p$ (like an electron) has a wavelength $\lambda$ associated with it.
D $\rightarrow$ II: The Compton effect describes the increase in wavelength of X-rays when they collide with electrons. Since this involves a billiard-ball-like collision, it confirms the Particle nature of light.
Step 4: Final Answer:
The correct match is A-IV, B-III, C-I, D-II.