Question: Q. 4. Find the ratio of de-Broglie wavelengths associated with two electrons accelerated through $25 \mathrm{~V}$ and $36 \mathrm{~V}$.
A [OD Comptt. I, II, III 2013]
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Solution:
Ans.
$$ V_{1}=25 \mathrm{~V}, V_{2}=36 \mathrm{~V} $$
de-Broglie wavelength of an electron
$$ \begin{array}{ll} \lambda & =\frac{1.227}{\sqrt{V}} \Rightarrow \lambda_{1}=\frac{1.227}{\sqrt{V_{1}}} \ \text { and } & \lambda_{2}=\frac{1.227}{\sqrt{V_{2}}} \ \therefore & \frac{\lambda_{1}}{\lambda_{2}}=\sqrt{\frac{V_{2}}{V_{1}}}=\sqrt{\frac{36}{25}} \ \Rightarrow \quad \frac{\lambda_{1}}{\lambda_{2}}=\frac{6}{5} \tag{1} \end{array} $$
