Answer :

Now we know de Broglie wavelength of a Particle is given by relation


𝜆 = h/mv


Where 𝜆 is de Broglie wavelength of the particle having mass m and moving with velocity v


But we know momentum is given by relation


p = mv


So, substituting we get de Broglie wavelength of Particle as


𝜆 = h/p


Or we can say momentum of particle is


p = h/ 𝜆


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


So substituting we get



or


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


so putting P = h/ 𝜆


we get kinetic energy of particle as



Where h is the Planck’s constant, m is mass of particle having de Broglie wavelength 𝜆


(a) Now we are given an electron whose de Broglie Wavelength should be


𝜆 = 589 nm = 589 × 10-9 m


We know mass of electron is, m = 9.1 × 10-31 Kg


and value of Planck’s constant, h = 6.6 × 10-34Js


putting values in the relation to find the kinetic energy of electron K we get




So kinetic energy of the electron is 6.9 × 10-25J


Converting it to eV


1 eV = 1.6 × 10-19J


i.e.


1J = (1/1.6 × 10-19)eV


So we get kinetic energy of electron as



Or we get Kinetic energy of electron as 4.31𝜇eV


(b) Now we are given an neutron whose de Broglie Wavelength should be


𝜆 = 589 nm = 589 × 10-9 m


We know mass of electron is


m = 1.66 × 10-27 Kg


and value of Planck’s constant


h = 6.6 × 10-34Js


putting values in the relation to find the kinetic energy of neutron K we get




So kinetic energy of the electron is 3.78 × 10-28J


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



Or we get Kinetic energy of electron as 2.36 neV


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