Calculate the wavelength of a neutron with a translational kinetic energy equal to KT at 300k​

Mark me brill plz

Explanation:

you have E= mv^2 /2

so v^2 = 2E/m  m of neutron =1.67 10^(-27) kg  

so v^2 = 2E/m     E = kT = 1.38 10^-23*300 =4.14 10^(-21) J

v^2 = 2*4.14 10^(-21)/1.67 10^(-27) =4.96 10^6 m^2s^-2

v=2.227 10^3 m/s

And

lambda = 6.6210^(-34)/(2.22710*3)*1.67 10^(-27)  

lambda=1.78 10^(-10)m =0.178 nm

please verify the calculus

the temperature of the gas, in k, not celsius.