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,
$λ = \frac {h}{mv}$
Given,
Kinetic energy (K.E) of the electron = 3.0 × 10-25 J
Since $K.E. = \frac 12 mv^2$
∴ Velocity $v = \sqrt {\frac {2K.E}{m}}$

$v= \sqrt {\frac {2(3.0 × 10^{-25} J)}{9.10939 × 10^{-31}kg}}$
$v= \sqrt { 6.5866×10^4}$
$v = 811.579 \ ms^{-1}$
Substituting the value in the expression of λ:
$λ = \frac {6.626×10^{-34} Js}{(9.10939 × 10^{-31} kg) (811.579 \ ms^{-1})}$
$λ = 8.9625×10^{-7} m$

Hence, the wavelength of the electron is $8.9625×10^{-7} m$.