Question

According to de-Broglie hypothesis, the wavelength associated with moving electron of mass $m$ is ${\lambda }_e$ . Using mass energy relation and Planck’s quantum theory, the wavelength associated with photon is ${\lambda }_p$. If the energy $(E)$ of electron and photon is same then relation between ${\lambda }_e$ and ${\lambda }_p$ is

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

Answer 1

Answer: (B)

${\lambda }_e=$ wavelength of the electron
${\lambda }_p=$ wavelength of the proton
$E_p=hv=\frac{hc}{{\lambda }_p}$
$E_e=hv=\frac{hc}{{\lambda }_e}$
$E_p=E_e$
$\to \frac{hc}{{\lambda }_p}=\frac{hc}{{\lambda }_e}$
$\to {\lambda }_p\propto {\lambda }_e$