A photon and an electron (mass m) have the same energy E. The ratio (photonelectron) of their de Broglie wavelengths is: (c is th…

Question

A photon and an electron (mass m) have the same energy E. The ratio (photonelectron) of their de Broglie wavelengths is: (c is the speed of light)

1. A. E/2m
2. B. c√2mE
3. C. c2m/E (Correct answer)
4. D. 1/cE/2m

Correct Answer

Option C — c2m/E

Detailed Solution & Explanation

The correct answer is $c\sqrt{\dfrac{2m}{E}}$.

Key Points

• Photon: $E=\dfrac{hc}{\lambda_{ph}}\Rightarrow\lambda_{ph}=\dfrac{hc}{E}$.
• Electron: $E=\dfrac{p^2}{2m}\Rightarrow p=\sqrt{2mE}$, so $\lambda_e=\dfrac{h}{\sqrt{2mE}}$.
• Ratio: $\dfrac{\lambda_{ph}}{\lambda_e}=\dfrac{hc/E}{h/\sqrt{2mE}}=\dfrac{c\sqrt{2mE}}{E}=c\sqrt{\dfrac{2m}{E}}$.