Find the wavelength of the particle

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  • #1
fluidistic
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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 [tex]\lambda _B=\frac{h}{mv}[/tex] where m is the relativistic mass, i.e. [tex]m=\gamma m_0[/tex].
Maybe [tex]F=qE[/tex]?

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.
[tex]\Delta V =\int _A^b \vec E d \vec l[/tex]... I don't go anywhere that way.
I've no idea what I'm missing.
 

Answers and Replies

  • #2
rock.freak667
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The energy produced by the pd is Ve, which is converted into ke of the particle (0.5mv2).
 
  • #3
fluidistic
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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 [tex]c^2 (m-m_0)[/tex]? 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
rock.freak667
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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).
 
  • #5
fluidistic
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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.
 

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