Coulombs law, initial speed to collide with other nucleus

AI Thread Summary
A helium nucleus with a radius of 1.9 fm and mass of 6.6 × 10^-27 kg must achieve a specific initial speed to collide with a fixed gold nucleus. The potential energy was calculated using Coulomb's law, yielding a value of 4.51 × 10^-12 J. The initial speed was derived as approximately 3.697 × 10^7 m/s, but this differed from the teacher's answer of 1.17 × 10^6 m/s. The discrepancy was attributed to a potential error in the mass used, suggesting the teacher may have used 6.6 × 10^-24 kg instead of the correct value. The correct calculations confirmed the initial speed needed for the collision.
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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.
 
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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.
 
Last edited:
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...
 
I've got the same answer as yours
 
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