# B DeBroglie Wavelength with Relativistic Electron

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1. Mar 24, 2016

### Oaxaca

I am trying to find the DeBroglie wavelength of an electron moving at .8c. I have never learned special relativity but I believe the momentum is affected (mass change). I used the formula p= (mv)/(1-v^2/c^2) and got a momentum of p = 2.733 E-22 and a wavelength of lamda = 2.4149 E-12. Did I apply the formula correctly for the relativistic momentum?

Thanks for any help

2. Mar 24, 2016

### Staff: Mentor

Neither $p=2.733\times{10}^{-22}$ grain-furlongs per fortnight nor $\lambda=2.4149\times{10}^{-12}$ parsecs would be correct, but I'm pretty sure you didn't use those units. What units did you use?

The $m$ in the formula you cite is the rest mass, not the relativistic mass (and we have a FAQ on why relativistic mass is seldom used - look for a link to it in the sticky thread at the top of this forum). As long as you get that right and pay attention to the units, you should come to the right answer.

3. Mar 24, 2016

### Oaxaca

I used kg and m/s for the electron, with momentum therefor being kg*m/s - and meters for my wavelength. Thanks for the response!

4. Mar 25, 2016

### vanhees71

The correct formula is
$$\vec{p}=\frac{m \vec{v}}{\sqrt{1-\vec{v}^2/c^2}}.$$
I'm to lazy to check your formula with quantities given in SI units which are not very intuitive to use in high-energy physics and thus why I've never seen anybody using them there in scientific work in this field ;-)).