Solution:
Solution
For proton, $$\lambda_p =\dfrac{0.286\times 10^{-10}}{\sqrt{\nu }}\ m$$
where V is p.d
For $$\alpha -particle,\ \lambda_\alpha =\dfrac{0.101\times 10^{-10}}{\sqrt{\nu }}m$$
so, keeping same $$\alpha $$ for proton and $$\alpha -partside$$
$$1= \dfrac{\lambda _p}{\lambda _{\alpha }} = \dfrac{0.286 \times \sqrt{V_{\alpha }}}{0.101 \times \sqrt{V_{P}}}$$
$$0.101 \times \sqrt{V_{P}} = 0.286 \times \sqrt{V_{\alpha }}$$
$$(0.101)^{2} \times V_{P} = (0.286)^{2}V _{\alpha} $$
$$\dfrac{(0.101)^{2}\nu }{(0.286)^{2}} = V _{\alpha }$$
$$(\because V_{P}=V)$$
$$\Rightarrow V_{\alpha } = \dfrac{V}{8} volt$$