Question

The de Brogue wavelengths for an electron and a photon are ${\lambda }_e$ and ${\lambda }_p$ respectively. For the same kinetic energy of electron and photon. which of the following presents the correct relation between the de Brogue wavelengths of two ?

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

Answer 1

Answer: (A)

${\lambda }_e=\frac{h}{\sqrt{2mk}}$
Also for photon $k=\frac{hc}{{\lambda }_p}$
${\lambda }_e=\frac{h\sqrt{{\lambda }_p}}{\sqrt{2mhc}}$
${\lambda }_p\propto \lambda e^2$