Question

A proton has kinetic energy $E=100keV$ which is equal to that of a photon. The wavelength of photon is ${\lambda }_2$ and that of proton is ${\lambda }_1$. The ratio of ${\lambda }_1/{\lambda }_2$ is proportional to

• A. $E^2$
• B. $E^{1/2}$
• C. $E^{-1}$
• D. $E^{-1/2}$

Answer 1

The correct option is B $E^{1/2}$

For proton and photon wavelength is given as $\to$ ${\lambda }_{proton}=\frac{h}{\sqrt{2mE}}$

${\lambda }_{photon}=\frac{h_c}{E}$

$\therefore$ the ratio of $\frac{{\lambda }_1}{{\lambda }_2}\Rightarrow E^{1/2}$