Question

What is the wavelength of an electron traveling at `5.01 times 10^5` `m``/``s`?

Answer 1

`1.45` nanometres

Explanation:

We can find the wavelength of the electron using De Broglie's formula, that is

`lambda=h/(mv)`

`lambda` is the wavelength in metres

`h` is Planck's constant which is around `6.626*10^-34 J\ s`

`m` is the mass of the object in kilograms

`v` is the velocity of the object in metres/second

Plugging in for `h=6.62*10^-34`, `m=9.11*10^-31` (mass of the electron), and `v=5.01*10^5`, we get

`lambda=(6.62*10^-34)/(9.11*10^-31*5.01*10^5)=1.45*10^-9 m`

`1.45*10^-9 m = 1.45nm`

So, the wavelength of an electron traveling at `5.01*10^5 m"/"s` would be `1.45` nanometres.