* De Broglie Wavelength: The concept of wave-particle duality states that all matter exhibits wave-like properties. The wavelength of a particle is given by the de Broglie equation:

λ = h / p

Where:

* λ is the wavelength

* h is Planck's constant (a very small value)

* p is the momentum of the particle (mass x velocity)

* Momentum and Wavelength: The equation shows that wavelength is inversely proportional to momentum. This means:

* Higher momentum = Smaller wavelength

* Lower momentum = Larger wavelength

* Proton vs. Golf Ball:

* Proton: Protons are incredibly small and have a tiny mass. Even at a slow speed, their momentum is relatively low. This results in a larger wavelength.

* Golf Ball: A golf ball is much larger and heavier. Even at a high speed, its momentum is significantly higher than a slow-moving proton. This means the golf ball's wavelength will be much smaller.

In summary: Even though a golf ball is moving much faster, the proton's smaller mass and lower momentum result in a significantly larger wavelength.