Finding Electron Speed and Wavelength

[purecp]

Homework Statement

The wavelength of an electron is 4.4 × 10−7 m.
How fast is it moving? The Planck’s con-
stant is 6.62607 × 10−34 J · s .
Answer in units of m/s.
013 (part 2 of 2) 10.0 points
If the electron has a speed of 9 × 106 m/s,
what is its wavelength?
Answer in units of m.

Homework Equations

Thats what I need help on.

The Attempt at a Solution

I tried E = hc / λ
Then E = 1/2mv^2

But that didnt work. Any ideas? Thanks

 

[ehild]

Use the de Broglie relation between momentum p and wavelength λ:

λ=h/p.

ehild

 

[Axiom17]

OK you're not too far off the right method so that's good

So these are the things you already know:

Planck's Constant: $h=6.62607\times 10^{-34} J s^{-1}$

Electron Wavelength: $\lambda_{e} = 4.4\times 10^{-7} m$

For the first part you need to find the velocity of the electron.

As ehild said you should use the de-Broglie relation for the wavelength of an electron, which is:

$$\lambda = \frac{h}{p}$$

You can just quickly look up the mass of an electron (if you can't remember it) and then you know everything you need to know in order to calculate the speed of the electron, through inputting the values and rearranging the equation.

For the second part you are now given the electron speed and need to find wavelength. This is a similar method just slightly different.

So now you know:

Electron Speed: $v = 9\times 10^{6}ms^{-1}$

Again you can use the de-Broglie relation, just rearrange it as required, input values, and there you go.