Answer :

(a) In order to find momentum, we know de Broglie wavelength for any particle is given by


𝜆 = h/P


Or P = h/𝜆


Where h is Planck’s constant


h = 6.63 × 10-34 Js


and P is the momentum of particle


here we are given the de Broglie wavelength


𝜆 = 1.00 nm = 1.00 × 10-9 m


Note: we can see that momentum only depends on de Broglie wavelength and Planck’s Constant which is same for both electron or Photon(Light Particle) so the momentum for both will also be same


Putting values we get momentum



So momentum of electron and photon is 6.63 × 10-25Kgms-1


(b) we know energy of an photon is given by the relation


E = hc/𝜆


Where E is the energy of Photon having wavelength 𝜆 and speed c,h is Planck’s constant


h = 6.63 × 10-34 Js


Speed of light or photon in free space


c = 3 × 108 m/s


And we are given wavelength


𝜆 = 1.00 nm = 1.00 × 10-9 m


Putting these values we get



Converting it to eV


We know


1 eV = 1.6 × 10-19J


i.e.


1J = (1/1.6 × 10-19)eV


So we get energy of Photon as



so we get energy of Photon as 1.24KeV


(c) We know kinetic energy of a particle is given by the relation



Where K is the kinetic energy of a particle of mass m moving with velocity v


Now multiplying L.H.S. and R.H.S. of the equation by m we get



or


But we know momentum is given by relation


P = mv


Where m is mass of Particle moving with velocity v


So substituting we get



or we get kinetic energy of particle K in terms of momentum P and mass of particle m as



The particle is electron and mass of electron is


m = 9.1 × 10-31Kg


Here the momentum of electron


P = 6.63 × 10-25Kgms-1


Putting these values in above equation we have



Converting it to eV


We know


1 eV = 1.6 × 10-19J


i.e.


1J = (1/1.6 × 10-19)eV


So we get Kinetic energy of electron as



so we get Kinetic energy of electron as 1.51eV


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