Question

I have been trying to figure out the solution to this problem of finding the velocity of de-Broglie's wave. I have tried to see answers from countless sources but none of them helped. My book provides me with the solution that : v = (hf)/(mc) . Where m is the mass of particle , f is the frequency, h is Planck constant and c is speed of light.

And this came from the fact that they used the formula c = f×(lambda) and substituted it in de-Broglie's equation for wavelength of a particle (= h/p) , which is really absurd to me as to why does the speed of light come here? Shouldn't it be v(wave)= f×(lambda) . Now I've also read that it has something to do with group velocity of matter waves but none of the sources which I read really explained as to why speed of light should be at play here. Can anyone explain this?

Answer 1

The equation v = (hf)/(mc) is derived from de Broglie's equation, where h is Planck's constant, f is the frequency, m is the mass of the particle, c is the speed of light, and v is the velocity of the particle.

Step-by-step explanation:

The equation v = (hf)/(mc) is derived from de Broglie's equation, where h is Planck's constant, f is the frequency, m is the mass of the particle, c is the speed of light, and v is the velocity of the particle.

The speed of light appears in this equation because it relates to the wavelength of the particle.

Using the equation c = λv, where c is the speed of light and λ is the wavelength, we can substitute this expression for λ in de Broglie's equation to obtain v = (hf)/(mc).