Question

Question #8fa9a

Answer 1

`3.28 * 10^(-10)"m"`

Explanation:

First thing first, you need to know the mass of the electron in order to be able to calculate its wavelength.

The mass of the electron is listed as

`m_"electron" = 9.10938356 * 10^(-31)"kg"`

Now, the wavelength of a particle of mass `m` that's moving at a speed `v` can be calculated using the de Broglie equation, which looks like this

`color(blue)(lamda = h/(m * v))" "`, where

`lamda` - the wavelength associated with the particle
`h` - Planck's constant, equal to `6.262 * 10^(-34)"kg m"^2 "s"^(-1)`

SIDE NOTE You'll often see this equation written like this

`lamda = h/p`

Here `p = m * v` represents the impulse of the particle.

So, plug in your values and solve for `lamda`, the wavelength of the electron

`lamda = (6.626 * 10^(-34)color(red)(cancel(color(black)("kg"))) "m"^color(red)(cancel(color(black)(2))) color(red)(cancel(color(black)("s"^(-1)))))/(9.10938356 * 10^(-31)color(red)(cancel(color(black)("kg"))) * 2.22 * 10^(6)color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))`

`lamda = 3.2765 * 10^(-10)"m"`

Rounded to three sig figs, the number of sig figs you have for the speed of the electron, the answer will be

`lamda = color(green)(3.28 * 10^(-10)"m")`