Calculate the wavelength of a neutron with a transitional kinetic energy equal to kT at 300K.?

Question

this problem deals with the wave character of particles.

we are given the equation lambda=h/p, where h is planks constant and p is the linear momemtum (de Broglie relation)

Answer 1

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

Answer 2

I would but it's just too simple.