<P> De Broglie followed his initial hypothesis of a periodic phenomenon, with frequency ν, associated with the energy packet . He used the special theory of relativity to find, in the frame of the observer of the electron energy packet that is moving with velocity v (\ displaystyle v), that its frequency was apparently reduced to </P> <Dl> <Dd> f = ν 0 1 − v 2 c 2 . (\ displaystyle f = \ nu _ (0) (\ sqrt (1 - (\ frac (v ^ (2)) (c ^ (2))))) \, .) </Dd> </Dl> <Dd> f = ν 0 1 − v 2 c 2 . (\ displaystyle f = \ nu _ (0) (\ sqrt (1 - (\ frac (v ^ (2)) (c ^ (2))))) \, .) </Dd> <Dl> <Dd> λ f = E / p = v p . (\ displaystyle \ lambda f = E / p = v_ (\ mathrm (p)) \, .) </Dd> </Dl>

The wavelength of a moving particle is directly proportional to its velocity