Shivam had knowledge that energy and momentum of an electron are related to frequency and wavelength of the associated matter (de-Broglie) wave by the relations, E = hv, p = h/λ . But when he heard from his friend that value of λ is physically significant but the value of frequency v has no physical significance. Shivam requested Shubham to explain such thing clearly. Shubham said to him that according to de Broglie, a particle behaves as a wave, but it is now established that a particle cannot be equivalent to a single wave, but it is equivalent to a group of waves or a wave packet. As = h/λ , so in the discussion of matter waves, a wave packet is significant and hence only wavelength, λ is significant. As, a single wave is insignificant, so phase velocity (velocity of a single wave, V = vλ,) is insignificant and thus, frequency v is also insignificant.
(a) What are the values shown by Shubham ?
(b) Calculate the
(i) momentum and
(ii) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V
