• Support PF! Buy your school textbooks, materials and every day products Here!

De broglie wavelength

  • Thread starter ariana13
  • Start date
  • #1
8
0
How do you calcuate at what energy do a photon and an electron have the same de broglie wavelength?
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
How do you calculate at what energy do a photon and an electron have the same de broglie wavelength?
Hi ariana13 and welcome to PF,

I'm assuming that this is a homework question, in which case for future reference we have Homework & Coursework problems for such questions. Don't worry about it now, your thread will get moved there in due course.

Now for your question. What do you know about the de Broglie wavelength? How is it claculated?
 
  • #3
8
0
Sorry if I put this in the wrong thread! For a photon, wavelength is just lambda=h*c/energy. I think for an electron you use the relativistic equation lambda=h/mv*sqt(1-v^2/c^2). I've tried equating these, but i ended up with a horrible equation to solve because i don't have velocity of the electron. I think i must have gone wrong somewhere.
 
  • #4
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
Since we are taking about energies here, it may be more useful to use an alternative form for the de Broglie wavelength for the electron,

[tex]\lambda = \frac{hc}{pc} = \frac{hc}{\sqrt{T^2+2Tm_0c^2}}[/tex]
 
  • #5
8
0
Thanks for your help. Sorry if this is a stupid question, but i've never seen that equation before, where does it come from? What does T stand for?
 
  • #6
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
Thanks for your help. Sorry if this is a stupid question, but i've never seen that equation before, where does it come from? What does T stand for?
There are no stupid questions :smile:

Anyway, it comes from the relativistic energy eqaution,

[tex]E^2 = \left(pc\right)^2 + \left(m_0c^2\right)^2[/tex]

Where E it the total energy. In the expression in my previous post T represents the kinetic energy of the electron. Of course if one would prever to calculate the total energy of the electron (including rest energy) one may rewrite the previous equation,

[tex]\lambda = \frac{hc}{pc} = \frac{hc}{\sqrt{E^2 - m_0^2c^4}}[/tex]
 
  • #7
8
0
Thanks for clarifying that, i think i do it now. :)
 

Related Threads for: De broglie wavelength

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
573
  • Last Post
Replies
3
Views
2K
Top