Question

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

Answer 1

From de Broglie’s equation,
$\lambda =\frac{h}{mv}$
Given, Kinetic energy (K.E) of the electron = 3.0 × ${10}^{–25}$ J
Since K.E=$\frac{1}{2}m{v}^2\therefore Velocity\left(v\right)=\sqrt{\frac{2K.E}{m}}=\sqrt{\frac{2(3.0\times {10}^{-25}J)}{9.10939\times {10}^{-31}kg}}=\sqrt{6.5866\times {10}^4}v=811.579m{s}^{-1}$
Substituting the value in the expression of λ:
$\lambda =\frac{6.626\times {10}^{-34}Js}{(9.10939\times {10}^{-31}kg)\left(811.579m{s}^{-1}\right)}\lambda =8.9625\times {10}^{-7}m$
Hence, the wavelength of the electron is 8.9625 × ${10}^{–7}$ m.