Question

In nuclear reactors, neutrons travel with energies of 5 × 10^-21J. Find their speed and wavelength.

Answer 1

Data:

KE = 5 × 10^-21 J, m = 1.675 × 10^-27 kg, h = 6.63 × 10^-34 J.s

(i) KE = `1/2 "mv"^2 = 5 xx 10^-21`J

∴ v = `sqrt((2"KE")/"m") = sqrt(((2)(5 xx 10^-21))/(1.675 xx 10^-27))`

= 2.443 × 10³ m/s

This is the speed of the neutrons. The de Broglie wavelength associated with the neutron,

(ii) λ = `"h"/"mv" = (6.63 xx 10^-34)/((1.675 xx 10^-27)(2.443 xx 10^3))`

= 1.620 × 10^-10 m

∴ λ = 1.620 Å