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JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
An electron of mass \(m\) and a photon have same energy \(E.\) The ratio of de-Broglie wavelengths associated with them is
- A \({\left( {\frac{E}{{2m}}} \right)^{\frac{1}{2}}}\)
- B \(\;C{\left( {2mE} \right)^{\frac{1}{2}}}\)
- C \(\;\frac{1}{C}{\left( {\frac{{2m}}{E}} \right)^{\frac{1}{2}}}\)
- D \(\;\frac{1}{C}{\left( {\frac{E}{{2m}}} \right)^{\frac{1}{2}}}\)
Answer & Solution
Correct Answer
(D) \(\;\frac{1}{C}{\left( {\frac{E}{{2m}}} \right)^{\frac{1}{2}}}\)
Step-by-step Solution
Detailed explanation
For electron of energy \(E\) de-Broglie wavelength, \(\lambda_{e}=\frac{h}{p}=\frac{h}{\sqrt{2 m E}}\) For photon of energy, \(E=h v=\frac{h c}{\lambda_{p}}\) \({\Rightarrow \lambda_{p}=\frac{h c}{E}}\)…
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