Dual Nature Of Radiation And Matter

Concept: Wave nature explains interference and diffraction.

Step 1: Identify.
Diffraction is purely wave phenomenon.

Concept: For photon:

Step 1: Conclusion.
de-Broglie wavelength equals electromagnetic wavelength.

Step 1: Understanding the Concept:
The de Broglie wavelength ( ) of a particle is related to its momentum ( ) by the equation . Momentum can be expressed in terms of kinetic energy ( ) and mass ( ).

Step 2: Key Formula or Approach:
The relationship between momentum and kinetic energy is , which gives .
Substituting this into the de Broglie wavelength formula:


Step 3: Detailed Explanation:
For a proton with mass and kinetic energy , its de Broglie wavelength is:

For a neutron with mass and the same kinetic energy , its de Broglie wavelength is:

Taking the ratio of their wavelengths:

The mass of a neutron ( kg) is very slightly larger than the mass of a proton ( kg). For most approximate calculations in such problems, their masses are considered nearly equal ( ).
Therefore, .

Step 4: Final Answer:
The ratio is approximately .