Question

A proton is accelerated from rest through a potential difference V0 and gains a speed v0. If it were accelerated instead through a potential difference of 3V0, what speed would it gain? Group of answer choices

Answer 1

Answer:

$v_{0,new} = v0\sqrt{}2$

Explanation:

Initial work done on the proton is given by, $\DeltaW0 = q V_o$

we know that, $\DeltaW = \DeltaK.E$

$qV0 = (1/2) m v_0^2$

$v_0 = \sqrt{}2 q V_0 / m$                                                        { eq.1 }

If it were accelerated instead through a potential difference of 2V0, then it would gain a speed will be given as :

using the above formula, we have

$v_{0,new} = \sqrt{}2 q (2V0) / m$    

$v_{0,new} = \sqrt{}4 q V0 / m$    

$v_{0,new} = v0\sqrt{}2$