# Find the wavelength of the particle

Gold Member

## 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.

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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).

Gold Member

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).

Gold Member

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.