Minimum Distance of Alpha Particle to Radium Core?

[anachin6000]

At what minimum distance can a particle 4α2, with kinetic energi Ec=4.77MeV, approach to a radium core 226Ra88.

This is how I solved it:
From energy conservation: ΔEc+ΔEp=0

Ec=[(Z1*Z2*e2)/(4*∏*ε)]*(1/r2-1/r1)

r2=1/[1/r1+4*∏*ε*Ec/(Z1*Z2*e2)] (1)

dr2/dr1=0 ⇔ r1→∞ (2)

From (1) and (2) ⇔ r2=1/[4*∏*ε*Ec/(Z1*Z2*e2)]

Now the problem is that in the book the correct answer is half of mine. Can someone help me to understand why?

 

[Simon Bridge]

Closest approach is the dead-on approach.

I'm not following your reasoning.

You want to find when the PE is the same as the KE.
Fix the Ra nucleus at the origin, so r is the distance from it to the alpha.
http://www.schoolphysics.co.uk/age1...ure/text/Alpha_particle_scattering/index.html