# An electron has a speed of 8.4 * 10^5 m s^-1. What is the de Broglie wavelength of this electron?

May 26, 2016

The de Broglie wavelength is 0.87 nm.

#### Explanation:

The de Broglie wavelength (λ) is given by

color(blue)(|bar(ul(color(white)(a/a) λ = h/(mv)color(white)(a/a)|)))" "

where

$h = \text{Planck's constant" = 6.626 × 10^"-34"color(white)(l) "kg·m"^2"s"^"-1}$
$m = \text{mass of electron" = 9.109 × 10^"-31"color(white)(l) "kg}$
$v = \text{velocity}$

λ = h/(mv) = (6.626 × 10^"-34" color(red)(cancel(color(black)("kg")))·stackrel("m")(color(red)(cancel(color(black)("m"^2)))}color(red)(cancel(color(black)("s"^"-1"))))/(9.109 × 10^"-31"color(red)(cancel(color(black)("kg"))) × 8.4 × 10^5 color(red)(cancel(color(black)("m·s"^"-1")))) = 8.7 × 10^"-10"color(white)(l) "m" = "0.87 nm"