Colliding Particles using energy

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The discussion revolves around calculating the distance of closest approach between a proton and an alpha particle, both initially moving towards each other at a speed of 3.9×10−3 c. Key concepts include the conservation of energy and momentum, with the hint suggesting that both must be considered in the solution. The initial attempt incorrectly assumed the final velocity at closest approach to be zero, leading to an incorrect distance calculation. Participants emphasize the importance of using the provided hints to arrive at the correct answer, which should be 1.3*10^-13. Understanding the conservation principles is crucial for solving the problem accurately.
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this question is from my previous assignment which was due 2 weeks back. just revising for mid-term not sure how to solve it. if someone explains it thoroughly it would be grate

Homework Statement


An alpha particle is a nucleus of Helium. It has twice the charge and four times the mass of the proton.

A proton and an alpha particle headed directly toward each other, had each initial speed of 3.9×10−3 c when they were far away.

Here, as is customary when describing processes involving nuclear targets, the speed is expressed as a fraction of c, the speed of light.

What is the distance of closest approach between the proton and the alpha particle?

Hint: There are two conserved quantities. Make use of both.



Homework Equations


U=Eqd or KqQ/r
K=1/2*(mv^2)

The Attempt at a Solution



.5m(v_i)^2 + Eq(d_i)= .5m(v_f)^2 + Eq(d_f)

where (V_f)=0 then i solved for (d_f)
and got the 1.87*10^-27 but the answer should be d_f=1.3*10^-13

could some 1 explain this to me and the reasoning! please
 
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You are assuming that V_f = 0. Make use of the hint that you were given.
 
this question is from my previous assignment which was due 2 weeks back. just revising for mid-term not sure how to solve it. if someone explains it thoroughly it would be grate
 
Why don't you make an attempt using the hints I just gave?
 
v_f is the final velocity , at minimum distance it can reach it will be zero.no?
 
seto6 said:
v_f is the final velocity , at minimum distance it can reach it will be zero.no?
No it won't. Use the hint that the problem gave you! What else is conserved besides energy?
 

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