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A proton and an alpha particle are accel...

A proton and an `alpha` particle are accelerated through the same potential difference V. The ratio of their de Broglie wavelengths is

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`lambda=(h)/(p)=(h)/(sqrt(2mqV))`
As `m_(alpha)=4m_(p)` and `q_(alpha)=2q_(p)`
`(lambda_(alpha))/(lambda_(p))=sqrt((2m_(p)q_(p))/(2m_(alpha)q_(alpha)))=sqrt((m_(p)q_(p))/(4m_(p)2q_(p)))=sqrt((1)/(8))`
`=(1)/(2sqrt2)`
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