PYQ NEET- Dual Nature Of Matter And Radiation L-8

Question: An electron of mass $m$ and a photon have same energy $E$. The ratio of de-Broglie wavelengths associated with them is#

A) $c(2 m E)^{\frac{1}{2}}$

B) $\frac{1}{c}\left(\frac{2 m}{E}\right)^{\frac{1}{2}}$

C) $\frac{1}{c}\left(\frac{E}{2 m}\right)^{\frac{1}{2}}$

D) $\left(\frac{E}{2 m}\right)^{\frac{1}{2}}$

Answer: $\frac{1}{c}\left(\frac{E}{2 m}\right)^{\frac{1}{2}}$#

Solution:#

For electron De-Broglie wavelength, $$ \lambda_{\mathrm{e}}=\frac{h}{\sqrt{2 m E}} $$

For photon of energy, $\mathrm{E}=\mathrm{h} \nu=\frac{h c}{\lambda_p}$ $$ \Rightarrow \lambda_{\mathrm{p}}=\frac{h c}{E} $$ $$ \therefore \frac{\lambda_e}{\lambda_p}=\frac{h}{\sqrt{2 m E}} \times \frac{E}{h c}=\frac{1}{c}\left(\frac{E}{2 m}\right)^{\frac{1}{2}} $$