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The kinetic energy of a slow moving neut...

The kinetic energy of a slow moving neutron is 0.04 eV. What fraction of the speed of light is the speed of this neutron ? At what temperature will the average kinetic energy of a gas molecule to equal to the energy of this neutron ? [ mass of neutron : `1.675xx10^(-27)` kg , Boltzmann constant, `k_B= 1.38xx10^(-23) J.K^(-1)` ]

Text Solution

Verified by Experts

Kinetic energy of the slow neutron =0.04 eV = `0.04 xx (1.6xx10^(-19))` J
Kinetic energy, `E_k=1/2mv^2`
`v=sqrt((2E_k)/m)=sqrt((2xx0.04xx1.6xx10^(-19))/(1.675xx10^(-27)))`
`=2764 m .s^(-1)`
`therefore v/c=2764/(3xx10^8) xx 100% ` = 0.00092%
Average kinetic energy at temperature T
`=3/2k_B T=0.04xx(1.6xx10^(-19))` J
`therefore T=(2xx0.04xx(1.6xx10^(-19)))/(3xx(1.38xx10^(-23)))`=309 K =`36^@C`
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