2.21 The mass of an electron is 9.1 × 10–31 kg. If its K.E. is 3.0 × 10–25 J, calculate its wavelength.

From de Broglie’s equation,
λ = hmv
Given,
Kinetic energy (K.E) of the electron = 3.0 × 10-25 J

Since K.E. = 12mv2
 Velocity v = 2K.E.m
   = 23.0 x 10-25 J9.10939 x 10-31 kg
   = 6.5866 x 104
v = 811.579 m/s

Substituting the value in the expression of λ:
λ = 6.626 x 10-34 Js9.10939 x 10-31 kg811.579 m/s
λ = 9.9625 x 10-7 m
Hence, the wavelength of the electron is 8.9625 × 10-7 m.