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
$E _{ p }= hv =\frac{ hc }{\lambda_{ p }}$
$E _{ e }= hv =\frac{ hc }{\lambda_{ e }}$
$E _{ p }= E _{ e }$
$\rightarrow \frac{ hc }{\lambda_{ p }}=\frac{ hc }{\lambda_{ e }}$
$\rightarrow \lambda_{ p } \propto \lambda_{ e }$