Question

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

Answer 1

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 = "Planck's constant" = 6.626 × 10^"-34"color(white)(l) "kg·m"^2"s"^"-1"`
`m = "mass of electron" = 9.109 × 10^"-31"color(white)(l) "kg"`
`v = "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"`