ExamBro
ExamBro
KCET · Physics · Dual Nature of Matter

An electron of mass \(m_{e}\) and a proton of mass \(m_{p}\) are moving with the same speed. The ratio of their de-Broglie's wavelengths \(\lambda_{e} / \lambda_{p}\) is

  1. A 1
  2. B 1836
  3. C \(\frac{1}{1836}\)
  4. D 918
Verified Solution

Answer & Solution

Correct Answer

(B) 1836

Step-by-step Solution

Detailed explanation

de-Broglie's wavelength,
\[
\lambda=\frac{h}{m v}
\]
For electron,
\[
\lambda_{e}=\frac{h}{m_{e} v}
\]
For photon,
\[
\lambda_{p}=\frac{h}{m_{p} v}
\]
\(\begin{aligned} \frac{\lambda_{e}}{\lambda_{p}} &=\frac{h / m_{e} v}{h / m_{p} v} \\ \frac{\lambda_{e}}{\lambda_{p}} &=\frac{m_{p}}{m_{e}} \\ \frac{\lambda_{e}}{\lambda_{p}}=\frac{1.67 \times 10^{-27}}{9.1 \times 10^{-31}} &=0.18 \times 10^{4}=1836 \end{aligned}\)