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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 :
$$\lambda = \frac{h}{p} = \frac{h}{mv}$$
$$\lambda \propto \frac{1}{v}$$
$$v_m = v - 20\% \text{ of } v = v - 0.20v = 0.80v = \frac{4}{5}v$$
$$\frac{\lambda_m}{\lambda_0} = \frac{v_0}{v_m}$$
$$\frac{\lambda_m}{\lambda_0} = \frac{v}{\frac{4}{5}v} = \frac{5}{4} = 1.25$$
$$\lambda_m = 1.25\lambda_0$$
$$\alpha = 1.25$$
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