Final answer:
The de-Broglie wavelength for a material particle of rest mass m0 and charge q accelerated from rest through a potential difference V relativistically is given by a formula that incorporates both relativity and quantum mechanics.
Step-by-step explanation:
The de Broglie wavelength, also known as matter waves, is a concept in quantum mechanics that states that all particles have a wavelength associated with them. The de-Broglie wavelength of a material particle of rest mass m0 and charge q accelerated from rest through a potential difference V relativistically is given by:
λ = h / √((2m0qV)/(qV + m0c^2))
Where:
- λ is the de-Broglie wavelength
- h is Planck's constant
- m0 is the rest mass of the particle
- q is the charge of the particle
- V is the potential difference
- c is the speed of light
This equation incorporates both relativity and quantum mechanics to accurately describe the behavior of matter waves.