The difference between two formulas for wavelength What is the difference between these formulas -
\begin{array}{l}
\lambda=\frac{h c}{E} \\
\text { and, } \lambda=\frac{h}{\sqrt{2 m k}}
\end{array}
There is a question -
Question: The debroglie wavelength of an electron is λ & has energy E.  How much extra energy should be given to the electron such that
its debroglie
wavelength is reduced by 25% now?
Which formula I have to use in this question ?
 A: One is for the wavelength in terms of energy for a light. That is, since $$E=h\nu$$ with $\nu$ being its frequency, $\lambda$ its wavelength, $c$ the speed of light. Now since $$c=\nu\lambda  \rightarrow \nu=\frac{c}{\lambda}$$ then $$E=\frac{hc}{\lambda}\rightarrow \lambda=\frac{hc}{E}\tag1$$
The next equation$^1$ $$\lambda=\frac{h}{\sqrt{2 m k}}\tag2$$ is the De Broglie wavelength $\lambda$ of a particle with mass $m$ in terms of (kinetic) energy $k$.
This would be all the information you need to solve your problem. You have one equation for the wavelength of light, and another for the wavelength of particles with mass.
$^1$Since
$$\lambda=\frac{h}{p}$$   then by comparing with equation (2) we get $$p=\sqrt{2 m k}$$  So $$p^2=2mk\rightarrow 
 k=\frac{p^2}{2m}$$
A: $\bullet$ Lets talk about the first equation $ \lambda = \frac{hc}{E}$, this equation is only true for a light. This equation gives the wavelength of a light wave with energy E. Now remember that for light $E=pc$ which gives us our equation in different form $\lambda=h/p$. In the era when duality of matter was just coming to be a concept, a physicist named de'Broglie gave a equation for wavelength of matter inspiring from this equation.
$\bullet$ De'Broglie stated that matter has a wavelength $\lambda_m$, m is used to not confuse between matter and light.$\lambda_m= \frac{h}{p}$. Remember that for a particle momentum $p=\sqrt{2mK}$, where $K$ is its kinetic energy. (Note that light doesn't have such a formula as m=0) which gives us our final equation $\lambda_m=\frac{h}{\sqrt{2mK}}$.
$\bullet$ This basically means first equation exclusively true for light and the second is true for matter.
