Question

Calculate the de broglie wavelength associated with an electron moving with velocity of 1/10 th the velocity of the light

Answer 1

Velocity of the electron $v = \frac{1}{10} \times c$

$v = \frac{1}{10} \times 3 \times 10^8 = 3 \times 10^7 \; m/s$

Mass of electron $m = 9.1 \times 10^{-31} \;kg$

De Broglie equation:

$λ = \frac{h}{p} = \frac{h}{mv}$

h – Plank’s constant

$h = 6.62 \times 10^{-34} \;Js$

p – momentum

v – velocity of electron

$λ = \frac{6.62 \times 10^{-34}}{9.1 \times 10^{-31} \times 3 \times 10^{7}}$

$λ = 2.24 \times 10^{-9}$

$10^{-9} \;m = nm$

$λ = 2.24 \;nm$