# Homework Help: De Broglie Wavelength from KE

1. Aug 10, 2012

### starthorn

1. The problem statement, all variables and given/known data
What is the De Broglie wavelength of an electron with KE= 8.5 eV?

2. Relevant equations
λ=h/p
KE=0.5mv2
p=mv

3. The attempt at a solution
I converted 8.5 eV into joules:
8/5 eV × 1.602e-19 J = 1.3617e-18

Then used it for KE to solve for v:
I got 1729006.11

Used v to get p:
9.11e-31 × 1729006.11 = 1.575e-24

Used p to get λ:
6.63e-34/1.575e-24

The answer required is on the order of picometers, and when I convert it to pm the answer is wrong. Entering it as it is also comes up wrong.
Sorry I use excessive sigfigs, my homework is through the Connect system for my textbook and there is a VERY SMALL margin of error so you always have to keep a bunch of extra or the answer might come up as wrong if you round too early.

2. Aug 10, 2012

### Nessdude14

You might need to use the relativistic momentum:
p=γm0v
(γ is the lorentz factor)

3. Aug 10, 2012

### Staff: Mentor

Are you sure it's not KE = 8.5 keV? Your calculations look OK.

What is it?

Ideally you should not round at all until you reach the final answer, i.e. keep the intermediate numbers in your calculator as you go along. Or better yet, derive an equation that lets you plug in your given numbers and get the final answer immediately. But I don't think that's your problem.

4. Aug 10, 2012

### starthorn

The hint portion of the problem states that it is not relativistic but I will check my calculations with it. Seeing as how the velocity I calculated is slightly under 0.006c though I am sure it is not.

Part a is in eV and part b is in keV, so yes I am sure

I can't see the answer without "giving up" on the problem, which means I will lose the credit for it. I know, it is an awful faulty system, but what can I do? It's the one my professor uses.

5. Aug 10, 2012

### Staff: Mentor

It's definitely not relativistic, as stated. 8.5 eV << 511 keV (the rest-energy of an electron).

Either you're missing something in the problem statement, or the answer in the "system" is simply wrong. Textbooks do sometimes have a wrong answer for a problem.

I tried using different units for the intermediate steps and I still get the same answer.

6. Aug 10, 2012