Question

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

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

Answer 1

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

${\lambda }_e=$ wavelength of the electron

${\lambda }_p=$ wavelength of the proton

$E_p=hv=\frac{hc}{{\lambda }_p}$

$E_e=hv=\frac{hc}{{\lambda }_e}$

$E_p=E_e$

$\to \frac{hc}{{\lambda }_p}=\frac{hc}{{\lambda }_e}$

$\to {\lambda }_p\propto {\lambda }_e$