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Q.
If $E$ and $\lambda$ represent the energy and wavelength respectively of an electron, then the graph between log $\lambda$ and $\log E$ will have
Dual Nature of Radiation and Matter
Solution:
$\lambda=\frac{h}{\sqrt{2 m E}} \Rightarrow \ln \lambda=\ln \left(\frac{h}{\sqrt{2 m}}\right)-\ln \sqrt{E}$
$\ln \lambda=\ln \left(\frac{h}{\sqrt{2 m}}\right)-\frac{1}{2} \ln E$ comparing with $y=m x+C$
$\ln \lambda$ vs $\ln E$ will have a slope of $-\frac{1}{2}$