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JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
An electron of mass \(m_{e}\) and a proton of mass \(m_{p}\) are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is
- A \(\sqrt{\frac{m_{p}}{m_{E}}}\)
- B \(\frac{m_{p}}{m_{E}}\)
- C \(1\)
- D \(\frac{m_{e}}{m_{p}}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{\frac{m_{p}}{m_{E}}}\)
Step-by-step Solution
Detailed explanation
\(\text { Kinetic Energy }=e \Delta \,V\) \(\lambda_{e}=\frac{h}{\sqrt{2 m_{e}(e \Delta V)}}\) \(\lambda_{p}=\frac{h}{\sqrt{2 m_{p}(e \Delta V)}}\) \(\Rightarrow \frac{\lambda_{e}}{\lambda_{p}}=\sqrt{\frac{m_{p}}{m_{e}}}\)
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