Find the ratio of wavelength of alpha particle and proton which have been accelerated from rest by same potential

Dear student,
 Using de-Broglie wavelength formula, we already know that proton and alpha particle are accelerated through the same potential.
So, both their velocities are same.
begin mathsize 12px style straight lambda equals fraction numerator straight h over denominator square root of 2 mV subscript straight o straight q end root end fraction so comma straight lambda space straight alpha space fraction numerator 1 over denominator square root of mq end fraction straight lambda subscript straight alpha over straight lambda subscript straight p equals square root of fraction numerator straight m subscript straight p straight q subscript straight p over denominator straight m subscript straight a straight q subscript straight a end fraction end root charge space on space alpha space particle space equals space 2 space straight x space charge space on space proton Also comma space mass space of space alpha space particle space equals space 4 space straight x space mass space of space proton straight lambda subscript straight alpha over straight lambda subscript straight p equals fraction numerator 1 over denominator 2 square root of 2 end fraction straight lambda subscript straight p equals space 2 square root of 2 space straight lambda subscript straight alpha end style
Regards

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