Coulombs law, initial speed to collide with other nucleus

[skate_nerd]

Homework Statement

A helium nucleus has radius rHe = 1.9 fm, mass m = 6.6 × 10-27 kg, and charge +2e. A gold nucleus has charge +87e and radius rAu = 7.0 fm. What initial speed must a helium nucleus have if it is to come into contact with a fixed gold nucleus in a head on collision?

Homework Equations

U=k(q₁q₂)/(r₁+r₂)
U=(mv²)/2

The Attempt at a Solution

started by solving for potential energy by making U=k(q₁q₂/(r₁+r₂)) so i got U=4.51(10^-12) J.
Now setting this equal to (mv²)/2, i got
v=√(2U/m)=
and this came out as 3.697(10⁷) m/s.
The teacher's answer is 1.17(10⁶) m/s.
Could somebody help me find where i went wrong? this is due tomorrow i would be very grateful.

 

[TSny]

Your solution looks correct to me. The ratio of your answer to your teacher's answer is close to √1000. The mass of an alpha particle in grams is 6.6 x 10^-24 g. I wonder if your teacher used a mass of 6.6 x 10^-24 kg rather than 6.6 x 10^-27 kg. That would account for the difference.

 

[skate_nerd]

Hm, that's interesting. I plugged in the 6.6(10^-24) and got the answer the teacher provided. Thanks for noticing that. I guess I'll email him now...

 

[jaumzaum]

I've got the same answer as yours