### Deriving De Broglie's Equation

Posted:

**Sun Oct 13, 2019 8:35 pm**Using the equations c=λv, E=mc^2, and E=hv, how can you derive De Broglie's equation?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=18&t=47366

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Posted: **Sun Oct 13, 2019 8:35 pm**

Using the equations c=λv, E=mc^2, and E=hv, how can you derive De Broglie's equation?

Posted: **Sun Oct 13, 2019 8:43 pm**

how i did it is i used the equations E=pc, E=hv, and c=hv:

you first convert c=hv to v=c/λ

Then substitute v=c/λ into the v in E=hv giving you E=h(c/λ)

then set E=pc equal to E=h(c/λ), giving you pc=h(c/λ)

the c cancel

giving you p=h/λ

solve for λ

λ=h/p

you first convert c=hv to v=c/λ

Then substitute v=c/λ into the v in E=hv giving you E=h(c/λ)

then set E=pc equal to E=h(c/λ), giving you pc=h(c/λ)

the c cancel

giving you p=h/λ

solve for λ

λ=h/p

Posted: **Sun Oct 13, 2019 8:56 pm**

Given that E=mc2 and E=hv

Substitute E to get mc2=hv

Rearrange to get mc = (hv)/c = p

Note: If E=pc, and E=hv, then p=E/c can be rearranged to p=hv/c

Given that c=λv and p=(hv)/c, p=h/λ

Which can be rearranged to λ=h/p (De Broglie)

Substitute E to get mc2=hv

Rearrange to get mc = (hv)/c = p

Note: If E=pc, and E=hv, then p=E/c can be rearranged to p=hv/c

Given that c=λv and p=(hv)/c, p=h/λ

Which can be rearranged to λ=h/p (De Broglie)