De Broglie Hypothesis

The de Broglie wavelength of a particle is related to its momentum by: where is Planck's constant. For a particle with kinetic energy , its momentum is:
Thus, the de Broglie wavelength is: Now, consider two particles, one with energy and the other with energy . The ratio of the wavelengths is:
Thus, the ratio of wavelengths is .

Concept:
Physics - Dual Nature of Radiation and Matter.
Step 1: Recall the de Broglie wavelength formula.
The de Broglie wavelength ( ) is related to the momentum ( ) of a particle: $ E E = \frac{1}{2}mv^{2} m p $