This gives you the electron's Compton wavelength, λ = ħ/mc.While deriving De-Broglie wavelength we equate mc^2 to hf
The De Broglie wavelength is a concept in quantum mechanics proposed by French physicist Louis de Broglie in 1924. It describes the wavelength of a particle, such as an electron, in motion.
The De Broglie wavelength is calculated using the following formula: λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.
The De Broglie wavelength is important because it helps to explain the wave-particle duality of matter. It shows that particles, such as electrons, can exhibit both wave-like and particle-like behavior.
According to the De Broglie hypothesis, all particles have a wavelength associated with them, including electrons. However, the De Broglie wavelength is inversely proportional to the mass of the particle, so the wavelength of an electron would be much smaller than that of a larger particle with the same rest energy.
The Heisenberg uncertainty principle states that it is impossible to know both the exact position and exact momentum of a particle at the same time. The De Broglie wavelength is related to this principle because it describes the uncertainty in the position of a particle due to its wave-like nature.