A Level Physics Practice Exam

Which equation relates momentum, Planck's constant, and wavelength?

1. E = mc^2

2. p = mv

3. p = h / wavelength

4. wavelength = h / p

The correct answer is: p = h / wavelength

The correct equation that relates momentum, Planck's constant, and wavelength is the equation where wavelength equals Planck's constant divided by momentum. This relationship arises from the de Broglie hypothesis, which states that all matter exhibits wave-like properties. In this context, momentum (p) can be defined as mass times velocity for macroscopic objects, but for particles at the quantum level, momentum is more directly related to their associated wave properties via Planck's constant (h). The equation wavelength equals h divided by p expresses how the wavelength of a particle is inversely proportional to its momentum. This highlights the wave-particle duality of matter, a fundamental concept in quantum physics. The equation demonstrates that as the momentum of a particle increases, its wavelength decreases, which is critical in understanding phenomena such as electron diffraction and the behavior of particles at the quantum scale. This is especially relevant in contexts where quantum effects are significant, such as in atomic and subatomic systems.