# Find the wavelength of the particle

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## Homework Statement

I'm not even sure the problem is about matterwave:
A particle of mass m and charge e is accelerated by a potential difference V. Find the wavelength of the particle. Show that this result agrees with the classical one when the non relativistic limit is taken.

## Homework Equations

Not sure, but I think that $$\lambda _B=\frac{h}{mv}$$ where m is the relativistic mass, i.e. $$m=\gamma m_0$$.
Maybe $$F=qE$$?

## The Attempt at a Solution

I'm not really sure how to find the motion equation of the particle and I need its velocity in order to calculate its de Broglie's wavelength. F=qE.
$$\Delta V =\int _A^b \vec E d \vec l$$... I don't go anywhere that way.
I've no idea what I'm missing.

## Answers and Replies

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rock.freak667
Homework Helper

The energy produced by the pd is Ve, which is converted into ke of the particle (0.5mv2).

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The energy produced by the pd is Ve, which is converted into ke of the particle (0.5mv2).
Thank you. Ah, very similar to an exercise I started 2 days ago and you helped me...
However isn't the kinetic energy worth $$c^2 (m-m_0)$$? Furthermore that would give a constant kinetic energy while they state "accelerated". Do they mean accelerated up to a speed v and then the particle maintains this speed constantly?!

rock.freak667
Homework Helper

Do they mean accelerated up to a speed v and then the particle maintains this speed constantly?!
I believe that is what it meant. I am not sure about the relativistic aspect though (never learned about it in depth).

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I believe that is what it meant. I am not sure about the relativistic aspect though (never learned about it in depth).
Thank you for all your help.