Why replace c with v in Broglie hypothesis I am in XI and I am currently studying atomic orbitals, I stumbled up and am stuck at the following step of de Broglie's hypothesis.

I did a little search on-line and found almost same derivation everywhere, the only place I found a more complex and supposedly accurate formula was the Wikipedia itself, though it did not explain the derivation.

Few such sites:


http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/02._Fundamental_Concepts_of_Quantum_Mechanics/De_Broglie_Wavelength
http://entrancechemistry.blogspot.in/2012/09/de-broglie-equation.html


In the derivation of the formula $$\frac{1}{\lambda}=\frac{h}{m\color{green}c}=\frac{h}{m\color{red}v}$$

we replace $c$ with $v$. I want to ask why?

As of Wikipedia it gives a better formula with the Lorentz factor $\gamma$ :- 

$$\frac{1}{\lambda}=\frac{h}{\color{red}\gamma m_oc}=\frac{h}{m_ov}  \sqrt{\color{red}1\color{red}-\frac{\color{red}v^\color{red}2}{\color{red}c^\color{red}2}}$$

Can anyone give the derivation or a hint or a logic that helps understand why the derivation from $E=mc^2$ and $E=h\nu$ gives the De Broglie equation.
C is for radioactive rays while v is for the matter waves..here c is for a particle travelling with light speed, i.e., radioactive rays, so we replace it with v velocity of any particle for its matter wave

$E=mc^2$ and $E=hv$. 
Therefore,  $$mc^2=hv$$
Or $$mc^2=\frac{hc}{k}$$, where k=wavelength
$$mc=\frac{h}{k}$$
Or, $$k=\frac{h}{mc}$$
   Replacing c by v we get
$$k=\frac{h}{mv}$$
Note the difference between matter waves and electromagnetic waves. E.W. are associated with electrical and magnetic field while matter waves are not so E.w. travel at 3×10^2 m/s. While matter waves travel with different velocity. The equation of de broglie with c is valid, it can be treated for finding the wavelength of electromagnetic waves, or electrons. But the velocity of matter waves are quite smaller as compared to light speed. So he used a general v in place of c V can be equal to c when the particle is travelling at light speed