What is the conclusion made by de Broglie? Write its mathematical relationship. [1+1]

Louis de Broglie proposed the dual nature of matter, extending the wave–particle duality concept from light to all moving particles. He concluded that matter exhibits both particle-like and wave-like properties, meaning every particle (e.g., electrons, protons) has an associated wave nature.

The mathematical relationship is given by the de Broglie wavelength equation: $$\lambda =\frac{h}{p}$$ where:

• $\lambda$ = wavelength of the particle (m),
• $h$ = Planck’s constant ($6.626\times 10^{-34}$ J·s),
• $p$ = momentum of the particle ($p=mv$, kg·m/s).

This equation shows that smaller, faster particles (e.g., electrons) have shorter wavelengths, linking their wave properties to their momentum.