Question

What is the wavelength of an electron with a mass of 9.11 x 10^-31 kg and a speed of 2.5 x 10^6 m.s^-1.?

Answer 1

1) The first step in the solution is to calculate the kinetic energy of the electron:

`K_E=1/2mv^2`
`E= 1/2*9.11*10^(¯31)kg*(2.5*10^6 m/s)^2`

`E = 2.84687*10^(¯17)kg*m^2 s^(¯2)` (I kept some guard digits)

When I use this value just below, I will use J (for Joules).

2) Next, we will use the de Broglie equation to calculate the wavelength:

`λ=h/p`
`λ=h/sqrt(2Em)`

`λ=(6.626*10^(¯34)J*s)/sqrt(2*(2.84687*10^(¯17)J)*(9.11*10^(¯31)kg))`

Now you can calculate final answer
Just to be sure about two things: (1) the unit on Planck's Constant is Joule-seconds, both are in the numerator and (2) there are three values following the radical in the denominator. All three of them are under the radical sign.