Challence problem on electric potential

[mrjoe2]

Edit to the title: CHALLENGE problem on electric potential energy*

Homework Statement

A proton and an alpha particle (q = +2e, m = 4u) are fired directly toward each other from far away, each with an initial speed of 0.010c. what is their distance of closes approach, as measured between their centers?

Homework Equations

u = proton mass = 1.67262158 × 10-27 kilograms
e = elementary charge = 1.60217646 × 10-19 coulombs
Kinetic energy Ke= 1/2 mv^2
U = Kq1q2/r
K = 9.0exp9
deltaKe + deltaU = 0

The Attempt at a Solution

(deltaKe1 + deltaU1) + (deltaKe2 + deltaU2) = 0 where 1 represents the u mass proton and 2 represents the alpha particle.
((0-.5u(.01c)^2) + (Ke*2e/r)) + ((0-2u(0.01c)^2) + (Ke^2e/r)) = 0
solve for r =2.45 *10^-14

the answer in the textbook is 1.93 * 10 ^-14

Iv done this over and over and over and am getting this 2.45 answer. please help! it is very frustrating! thanks!

 

[tiny-tim]

Hi mrjoe2!

A proton and an alpha particle (q = +2e, m = 4u) are fired directly toward each other from far away, each with an initial speed of 0.010c. what is their distance of closes approach, as measured between their centers?
…
((0-.5u(.01c)^2) + (Ke*2e/r)) + ((0-2u(0.01c)^2) + (Ke^2e/r)) = 0

ah … but they're not stationary at closest approach, are they?

 

[rl.bhat]

If you consider a proton and an alpha particle as a system, at the closest approach the total kinetic energy of the system is converted to the potential energy.
Hence
.5u(.01c)^2) + + 2u(0.01c)^2) = (Ke*2e/r))