When I am deriving de Broglie wavelength for a relativistic particle using $E^2=m^2c^4+p^2c^2$ and equating with $E=\frac{hc}{\lambda}$, and then putting $p=kmv$, $k$ being relativistic factor, I am getting $\lambda =\frac{h}{kmc}$ instead of $\frac{h}{kmv}$.
Is there any mistake that i am doing with equating those 2 energy equations ? Or something else ?
The equation $E^2=m^2c^4+p^2c^2$ is valid for all particles with mass $m$.
But equation $E=\frac{hc}{\lambda}$ is true only for massless particles (i.e. $m=0$), e.g. for photons.
I guess you got this wrong equation by putting together $E=h\nu$ (which is indeed correct for all particles) and $\nu=\frac{c}{\lambda}$ (which is valid only for massless particles).
The speed is $\frac{kmvc^2}{kmc^2}=\frac{pc^2}{E}$. Using this speed in place of $c$ to get frequency from a wavelength,$$E=h\nu=\frac{hpc^2}{E\lambda}\implies\lambda=\frac{hpc^2}{E^2}=\frac{hv}{kmc^2}.$$This is the correct relation for massive particles.
