Question

What is the de Broglie wavelength for an electron that travels at `90%` the speed of light?

Answer 1

See below

Explanation:

First we need to know the formula. It is, `λ = h/(mv)`
we know speed of light is `3.00 xx 10^8` `m`/`s`, then we need to find what `90%` of that is.
To find that we do this,

`0.90c = 3.00 xx 10^8 "m/s" xx 0.90`

`=2.7 xx 10^8` `"m"//"s"`

`λ = h/(mv)`

`λ=` wavelength

`h=` Planck's constant, which is `6.63 xx 10^-34` `"m"^2 cdot` `"kg"//"s"`

`m=` mass of electron, which `9.11 xx 10^-31 "kg"`

`v=` velocity

`lambda =(6.63 xx 10^-34 "kg"cdot"m"^2//"s") / ((9.11xx10^-31 "kg") xx (2.7xx10^8 "m/s"))`

`=> lambda= 2.70 xx 10^-12"m"`