Question

The wavelength ${\lambda }_e$ of an electron and ${\lambda }_p$ of a photon of same energy $E$ are related by

• A. ${\lambda }_p\propto {\lambda }_e^2$
• B. ${\lambda }_p\propto {\lambda }_e$
• C. ${\lambda }_p\propto \sqrt{{\lambda }_e}$
• D. ${\lambda }_p\propto \frac{1}{\sqrt{{\lambda }_e}}$

Answer 1

The correct option is A ${\lambda }_p\propto {\lambda }_e^2$

${\lambda }_p\alpha {\lambda }_e^2$

Wavelength of electron

${\lambda }_e=\frac{h}{\sqrt{2mE}}$ and proton ${\lambda }_p=\frac{h_c}{E}$

$\Rightarrow {\lambda }_e^2=\frac{h^2}{2mE}$ or $E=\frac{h_c}{{\lambda }_p}$

$\therefore$ ${\lambda }_e^2=\frac{h^2}{2m\frac{h_c}{{\lambda }_p}}$

$\Rightarrow {\lambda }_e^2=\frac{h^2}{2m{h}_c}{\lambda }_p$

${\lambda }_e^2\alpha {\lambda }_p$