11. Dual nature of radiation and matter — Physics STD 12 Science — Question

$\lambda=\frac{h}{\sqrt{2 m E}}=\frac{h}{\sqrt{2 m}} \cdot \frac{1}{\sqrt{E}}$

$\Rightarrow \log \lambda=\log \left(\frac{h}{\sqrt{2 m}} \cdot \frac{1}{E}\right)$

$\Rightarrow \log \lambda=\log \frac{h}{\sqrt{2 m}}+\log \frac{1}{E^{1 / 2}}$

$\Rightarrow \log \lambda=\log \left(\frac{h}{\sqrt{2 m}}\right)-\frac{1}{2} \log E$

$\Rightarrow \log \lambda=-\frac{1}{2} \log E+\log \frac{h}{\sqrt{2 m}}$

So, equation of straight line is $y=m x+c$.

This is equation of line with slope $-\frac{1}{2}$.