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 E_{K} 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

E_{k} = 6.21 × 10^{-21}J

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^{-27}Kg

Value of Planck’s constant

h = 6.63 × 10^{-34}Js

and kinetic energy of neutron is

E_{k} = 6.21 × 10^{-21}J

Putting values in above equation we get

Or 𝜆 = 0.146 × 10^{-9}m = 0.146 nm

So the de Broglie wavelength of neutron is 0.146 nm

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