Distance Problem Find Distance Between Alpha Particles

[mustang]

Problem.
Given= k_e=8.98755*10^9 Nm^2/C^2, q_p=1.6021*10^-19 C, and g=9.8 m/s^2.
Two alpha particles (helium nuclei), each consisting of two protons and two neutrons, have an electrical potential energy of 6.35*10^-19 J.
What is the distance between these particles at this time? Answer in m.
Note:I figure out that 1 alpha particle is 3.2*10^-19C. So using the Potential energy of electric formula I squared 3.2*10^-19. Afterwards I divided it by 6.35*10^-19 and multplied that by 8.98755*10^9C to get the answer of 1.45313788*10^-9C. However the answer was incorrect what did I do wrong?

 

[HallsofIvy]

It would be better to write the formula rather than just reciting what you did.

The formula for potential energy for two charged particles with distance r between them is: -(kq₁q₂)/r (then anti-derivative of the force function with respect to r).

You are given that k=8.99*10^9, that q₁ and q₂ are both equal to 3.2*10^-19C (actually, you are not given that, you are given that one proton is 1.6021*10^-19 C and an alpha particle has two protons so: 3.20*10^-19 C- Since the potential is given with only 3 sig. figures, I also rounded off k.)and, finally, the the potential is 6.35*10^-19.

That is, the equation says (8.99*10^9)(3.20*10^-19)(3.20*10^-19)/r=
6.35*10^-19 or (92.1*10^-29)/r= 6.35*10^-19. Then 92.1*10^-29= (6.35*10^-19)r so r= (92.1*10^-29)/(6.35*10^-19)= 14.5*10^-10 or
1.45* 10^-9 m.

There are two things wrong with your answer:
1) Since the potential was given with only 3 significant figures, you answer "1.45313788*10^-9" claims too much accuracy.
2) The problem asked for "distance" and specifically said "answer in m" but your answer is "1.45313788*10^-9C" giving the answer in Coulombs as if it were charge!

 

[mustang]

Formula

The formula for this equation is PE_electric=k_c*q1*q2/r. Also when I asked my teacher he said that he didn't get 1.45*10^-9C. He said that I did my math wrong.

 

[HallsofIvy]

Also when I asked my teacher he said that he didn't get 1.45*10^-9C. He said that I did my math wrong.

Well, that was pretty much what I said in (2) wasn't it? Please read my response again.