Question

Calculate the wave length s of the following cases : 1)neutrons thermally excited at T = 500 degrees K 2) electrons accelerated by a voltage of 50kV.

Answer 1

Answer.

First part

Energy of neutron (E)= 3kT/2 = 1/2mv²

V = (3kT/m)^1/2

Wavelength of the neutron = h/mv = h/(3mkT)^1/2

m = mass of neutron = 1.67 x 10^-27 kg

h = Plank constant = 6.627 x 10^-34 JS

k = Boltzman constant = 1.38 x 10^-23 JK^-1

Putting these values, wave length of neutron at 500K is = 1.127 x 10^-10 m (Ans)

Second part

Charge of an electron = 1.6 x 10^-19 C

Mass of the electron (m) = 9.11 x 10^-31 kg

Kinetic energy of the electron (E)= 1.6 x 10^-19  x 50 x 1000 J = 8 x 10^-15 J

Wavelength of the electron = h/(2mE)^1/2

h = Plank constant = 6.627 x 10^-34 JS

Putting these values, wavelength of the electron = 5.467 x 10^-12 m (Ans.)