Q17 / 170 · Manipal (MET) 2020 · Chemistry

The ratio of de-Broglie wavelengths for electron accelerated through 200 V and 50 V is

  • Correct answer
    A
    $1: 2$
  • B
    $2: 1$
  • C
    $3: 10$
  • D
    $10: 3$

Solution

$\lambda=\frac{h}{m v}=\frac{h}{\sqrt{2 m \times(\mathrm{KE})}}$ $\begin{aligned} \lambda_1 & =\frac{h}{\sqrt{2 m \times 200}} \\ \lambda_2 & =\frac{h}{\sqrt{2 m \times 50}} \\ \frac{\lambda_1}{\lambda_2} & =\frac{1 \times \sqrt{50}}{\sqrt{200 \times 1}}=\frac{1}{2} \\ \lambda_1: \lambda_2 & =1: 2\end{aligned}$

Hence, the correct answer is option: 'A'.

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