Question #8fa9a

1 Answer
Nov 11, 2015

#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.

physicstime.com

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")#