An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocit

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An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20\%$. The de Broglie wavelength of electron in the medium is $\alpha\lambda_{0}$, where $\lambda_{0}$ is its de Broglie wavelength in free space. The value of $\alpha$ is $\_\_\_\_$

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Sol. [Key Concept: $\lambda = \frac{h}{mv} \propto \frac{1}{v}$; reducing $v$ to $0.8v$ makes $\lambda ightarrow 1.25\lambda_{0}$, so $\alpha = 1.25$.]$$\ \lambda_{0} = \frac{h}{{mv}_{0}}$$$$\begin{matrix} & \lambda = \frac{h}{mv} = \frac{h}{	ext{ }m\left( 0.8v_{0} ight)} = \frac{1}{0.8}\frac{	ext{ }h}{{mv}_{0}} = 1.25\lambda_{0} \ & \ 	herefore\alpha = 1.25 \end{matrix}$$

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