De Broglie Hypothesis

We are given the following: - The mass of particle A is double that of particle B, so .
- The kinetic energy of particle B is that of A, so .
The de Broglie wavelength of a particle is given by the formula: where is Planck's constant and is the momentum of the particle. The momentum of a particle is related to its kinetic energy and mass by the equation: Thus, the momentum can be written as:
Step 1: Finding the momentum of particles A and B
For particle A, the momentum is: For particle B, the momentum is:
Step 2: Finding the ratio of the de Broglie wavelengths
Now, the de Broglie wavelength ratio for particles A and B is: Thus, the ratio of the de Broglie wavelength of A to B is , which corresponds to option (C).