An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)
Show Hint
- \(\frac{1}{c}\left(\frac{2m}{E}\right)^{1/2}\)
- \(\frac{1}{c}\left(\frac{E}{2m}\right)^{1/2}\)
- \(\left(\frac{E}{2m}\right)^{1/2}\)
- \(c(2mE)^{1/2}\)
The Correct Option is B
Solution and Explanation
Photon: \(E=\frac{hc}{\lambda_p}\), so \(\lambda_p=\frac{hc}{E}\).
Ratio: \(\frac{\lambda_e}{\lambda_p}=\frac{h}{\sqrt{2mE}}\cdot\frac{E}{hc}=\frac{1}{c}\frac{E}{\sqrt{2mE}}=\frac{1}{c}\sqrt{\frac{E}{2m}}\).
Answer: (2) \(\frac{1}{c}\left(\frac{E}{2m}\right)^{1/2}\)
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