# Calculating the wavelength of an electron

1. Jan 18, 2012

### bobsmith76

1. The problem statement, all variables and given/known data

Calculate the wavelength of a beta particle (electron) that has an energy of 4.35 × 104 eV

2. Relevant equations

E = hf
λ = h/mv
V = W/q
eV = .5mv^2

3. The attempt at a solution

I can't figure out how to get electron volts into a form of energy that I'm familiar with in an equation. I tried

eV = .5mv^2 , but that gave me a speed above the speed of light.

I also tried using E = hf, but that also gave me a ridiculous number.

2. Jan 18, 2012

### PeterO

The conversion factor for swapping between eV and Joules is 1.6 x 10-19.

You either divide or multiply depending which way you are changing.

You should know which figure is bigger: either a few joules = lots of eV or a few eV = lots of joules. You thus multiply or divide to get the size of answer you need.

Think: if you multiply by 1.6 x 10-19 will that give a bigger number or a smaller number? Dividing will give the opposite. What size of answer do you want?

3. Jan 18, 2012

### ehild

1 eV = elementary charge * 1 V=1.602 x 10-19 J.

Apply relativity theory. The given energy is the kinetic energy of the particle (the energy it gains when accelerated by 4.35 x 10 4 V. Find the relativistic momentum, and you get the wavelength as λ=h/p.

ehild

4. Jan 18, 2012

### bobsmith76

I can't get it. I'm pretty sure I have to divide 4.35 * 10^4 by 1.6 * 10^-19, but that gives me 2.7 *10^23. I then plug that into the equation

E/h = f

which gives me 56 orders of magnitude. I then divide 1.6 * 10^-19 by 4.35 * 10^4 and that also gives me the wrong answer. I have a feeling that my second step of using the

E/h = f equation is wrong.

5. Jan 18, 2012

### ehild

In what units? You have to get joules.

It is valid for photons. The electron is not photon.

What do you know about Relativity Theory?

ehild

6. Jan 18, 2012

### bobsmith76

ok, I got the joules to be 7.53 * 10^-18, using this website

http://www.unitconversion.org/energy/joules-to-electron-volts-conversion.html

I don't know how they got that number and would like to know. In any case, I then plugged that number into

.5mv^2 and E = mc^2, using 9.11*10^-31 for the mass. After I got v, I plugged that into

lambda = h/mv

and I was off by an order of magnitude, so I still am doing something wrong.

7. Jan 18, 2012

### ehild

8. Jan 18, 2012

See above