Q. 17 B3.8( 13 Votes )

# Also find the de

Answer :

Here the neutron is in thermal equilibrium with matter and it have a kinetic due which depends upon temperature of surrounding

We have a relation to find kinetic energy of a atomic particle at any Temperature which is Where EK is the kinetic energy of particle at temperature T and K is Boltzmann constant

K = 1.38 × 10-23 JK-1

Here temperature is

T = 300 K

So linetic energy of neutron is So kinetic energy of neutron is

Ek = 6.21 × 10-21J

And we know Kinetic energy of a particle is given by the relation Where vis the speed of the particle and m is the mass of the particle

Multiplying both side sides by m Or So we get We know de-Broglie wavelength of a particle is given by relation where 𝜆 is the de-Broglie wavelength of a particle having mass m and moving with velocity v, h is Planck’s constant

putting the value of in above equation we get de Broglie wavelength Here the particle is neutron and we know mass of neutron

m = 1.66 × 10-27Kg

Value of Planck’s constant

h = 6.63 × 10-34Js

and kinetic energy of neutron is

Ek = 6.21 × 10-21J

Putting values in above equation we get  Or 𝜆 = 0.146 × 10-9m = 0.146 nm

So the de Broglie wavelength of neutron is 0.146 nm

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