Quantum Physics

The wave theory of light successfully explains phenomena such as:

• Reflection: Wavefront bending at an interface.
• Refraction: Change in speed and bending of light at different media.
• Diffraction: Spreading of waves when they encounter obstacles.

However, the Compton effect involves the scattering of photons by electrons, which requires the particle nature of light (photons) and cannot be explained by the wave theory. Instead, it is explained using quantum mechanics.

Step 1: Understanding the Concept:
Every moving particle has an associated wave called the de Broglie wave. For a particle of mass and charge accelerated from rest through a potential difference , its kinetic energy determines its de Broglie wavelength.

Step 2: Key Formula or Approach:
De Broglie wavelength:

Step 3: Detailed Explanation:
For an electron: charge is , mass is .

For a proton: charge is , mass is .

Now, calculate the ratio :



Step 4: Final Answer:
The ratio of their de Broglie wavelengths is .