# For Deriving De Broglie' Wavelength

by puneeth
Tags: broglie, deriving, wavelength
 P: 9 1. The problem statement, all variables and given/known data The De Broglie Wavelength of any object in motion is given by $$\lambda$$=$$\frac{h}{P}$$ where h is Planck's constant and P is the body's momentum. for heavy masses this wavelength is too small to be observed, nevertheless it is still there.... I have seen a derivation for this which is not convincing and any clarification which is convincing will be received with thanks... 2. Relevant equations E=mc^2 E=h$$\nu$$ 3. The attempt at a solution The derivation is as follows -- from the above 2 equations mc^2 =h$$\nu$$ but $$\nu$$=c/$$\lambda$$ hence mc=h/$$\lambda$$ rearranging terms, $$\lambda$$=h/mc = h/p where p is the momentum of the body like electron travelling with high speed. the above relation can be used for finding the wavelength of a moving electron or even a slow moving proton - (as mass of proton is 1837 times electron for having the same momentum it travells at a speed 1837 times lesser than that of electron). how can we take momentum of any body in place of "p" in the formula when it is actually kept in the place of "mc"? during the derivation "c" is cancelled on both sides. if we actually begin the derivation taking a body travelling with speed "v" then we cannot cancel "c" and "v". the formula is applied even to electrons moving at "c/2" or "c/3" speeds. thus cancelling the speeds on both sides would be a really bad approximation. even the energy of a body travelling with c/3 etc would not turn out to be exactly mc^2. then how is the derivation valid? please clarify... i am unable to think it out