Distance Problem!

1. Jan 5, 2004

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?

2. Jan 6, 2004

HallsofIvy

Staff Emeritus
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.

1) Since the potential was given with only 3 significant figures, you answer "1.45313788*10^-9" claims too much accuracy.

3. Jan 6, 2004

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.

4. Jan 7, 2004

HallsofIvy

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