# Finding potential difference to accelerate the ion

#### jheld

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Kf + Uf = Ki + Ui
U = qV where V is potential difference (volts)

K = (1/2)mv^2

3. 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?

Last edited:

Correct.

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