What potential difference is needed to accelerate a he+ ion (charge +e, mass 4u) from rest to a speed of 1.5×106 m/s ? e?

We can solve the problem by using conservation of energy.

In fact, the electric potential energy lost by the charge when moving through the potential difference is equal to the kinetic energy acquired:

where is the final kinetic energy, and is the initial kinetic energy, which is zero since the particle starts from rest.

We can rewrite the equation above as:

where

is the charge of the ion

is the potential difference

is the mass of the ion

is the final speed of the ion

Substituting the numbers and rearranging the equation, we can find the potential difference needed: