Question

what is the ratio of velocity of electron to the proton when both are accelerated through the same potential​

Answer 1

Let us assume that the electron and proton were accelerate by the potential 'V'. Also, it is known that they have same charge , let it be 'q'. And, mass of proton = 1840 × mass of electron.

Now,

qv = kinetic energy of electron = kinetic energy of proton.

=>

$\frac{1}{2} m_{e} {( v_{e}) }^{2} = \frac{1}{2} m_{p} { (v_{p}) }^{2} \\ \\ = > { (\frac{ v_{e} }{ v_{p} } )}^{2} = \frac{ m_{p}}{ m_{e} } \\ \\ = > \frac{ v_{e} }{ v_{p} } = \sqrt{1840} \\ \\ = > \frac{ v_{e} }{ v_{p} } = 42.8$