Finding potential difference to accelerate the ion

[jheld]

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?

 

[wywong]

Correct.

 

[nlightner]

Your solution looks correct. The potential difference needed to accelerate the He+ ion to a speed of 2.0 * 10^6 m/s is approximately -83000 volts. This is a large potential difference, which makes sense since the ion has a relatively large mass and needs a lot of energy to accelerate to such a high speed.