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Q.
The log-log graph between the energy $E$ of an electron and its de-Broglie wavelength $\lambda$ will be
Dual Nature of Radiation and Matter
Solution:
$\lambda=\frac{h}{\sqrt{2 m E}}=\frac{h}{\sqrt{2 m}} . \frac{1}{\sqrt{E}}$
$\log \lambda=\log \frac{h}{\sqrt{2 m}}+\log \frac{1}{\sqrt{E}}$
$\Rightarrow \log \lambda=\log \frac{h}{\sqrt{2 m}}-\frac{1}{2} \log E$
$\Rightarrow \log \lambda=-\frac{1}{2} \log E+\log \frac{h}{\sqrt{2 m}}$
This is the equation of straight line having slope $(-1 / 2)$ and positive intercept on $\log \lambda$ axis.