In fission reactors, one deals with neutrons having kinetic energies as high as

Question

In fission reactors, one deals with neutrons having kinetic energies as high as 10 MeV. How much error is incurred in computing the speed of 10-MeV neutrons by using the classical expression rather than the relativistic expression for kinetic energy? For classical I used (1/2)mv^2 and got v=4.36244 x 10^7 m/s For relativistic, I used KE/(m_0*c^2)= (1/sqrt(1-(v/c)^2)-1) and found v to be 4.3279011 x 10^7 m/s I found the error with the classical v - relativistic v divided by relativistic v and found the percentage error to be 0.798087%. Does my method and numbers sound correct and reasonable?

Explanation / Answer

Method sounds correct. Though I got slightly different values.

vnewtonian=4.376x10^7 m/s

vrelativistic=4.342x10^7 m/s

%error = 0.783 %

Use mNc2=969.565 MeV (from wikipedia)

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