# Homework Help: Find the wavelength of the particle

1. Sep 15, 2010

### fluidistic

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

2. Relevant 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 $$F=qE$$?

3. 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.

2. Sep 15, 2010

### rock.freak667

Re: Matterwave

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

3. Sep 15, 2010

### fluidistic

Re: Matterwave

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?!

4. Sep 15, 2010

### rock.freak667

Re: Matterwave

I believe that is what it meant. I am not sure about the relativistic aspect though (never learned about it in depth).

5. Sep 15, 2010

### fluidistic

Re: Matterwave

Thank you for all your help.