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## Homework Statement

What potential difference is needed to accelerate a He + ion (charge +e, mass 4 u) from rest to a speed of 2.0 * 10^6 m/s?

## Homework Equations

Kf + Uf = Ki + Ui

U = qV where V is potential difference (volts)

K = (1/2)mv^2

## The Attempt at a Solution

I chose the rest point to be r = 0, so even with U = Kq_1q_2/r, it would equal zero at the start.

Then:

(1/2)mv^2 = -qV

V = (-1/2q)mv^2

= -(2q/)uv^2

m = u* 1.66*10^-27 kg/u = 1.66*10^-27 kg

V = -(2/(1.6*10^-19 Coulombs)) * (1.66*10^-27 kg)(2.0*10^6 m/s)^2

= -83000 volts

Is this right?

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