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


Where P is the momentum of particle having mass m and moving with velocity v


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


Here,


The de Broglie Wavelength is, 𝜆 = 1.40 × 10–10m


The particle is neutron and mass of neutron is, m = 1.66 × 10–27Kg


putting these values we get the kinetic energy of neutron as



So kinetic energy of the neutron is 6.75 × 10-21J


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 neutron as



Or we get Kinetic energy of neutron as 0.042 Ev


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