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

 

[Nickie]

Your solution looks correct. The only potential error could be in the conversion of units. Make sure you are using the correct unit conversions for the values given in the problem (i.e. fm to m, kg to g, etc.). Also, make sure you are using the correct value of the Coulomb constant, k, which is 8.99 x 10^9 Nm^2/C^2.

Another possibility is that your teacher may have rounded the answer to 1.17 x 10^6 m/s, which is equivalent to 1.17 x 10^6 m/s. Double check your calculations and units to make sure they are accurate. If everything checks out, then your answer should be correct.