Calculate the smallest possible distance between the two electrons

[XJellieBX]

Question:
Two electrons are fired at 3.5 x 10^6 m/s directly at each other.
(a) Calculate the smallest possible distance between the two electrons.

Attempt:
I tried Ee=Ek for this question and this is how it went.
Note*(q1=q2)

Ee=Ek
kq^2 = 0.5mv^2
r
r= kq^2
0.5mv^2
= (9.0x10^9(N x m^2)/C^2)(1.6x10^-19C)^2
0.5(9.1x10^-31kg)(3.5x10^6m/s)^2
= 4.1x10^-11m


I don't seem to be getting the right answer. Can someone please tell me what I'm doing wrong?

 

[hage567]

Your initial kinetic energy is not just 0.5mv^2, it's double that, since both electrons are moving. Try that.

 

[XJellieBX]

The answer still doesn't match, but I'm thinking the book is wrong. So thank you=)

 

[aq1q]

what is the answer?

 

[XJellieBX]

It says 4.5x10^-6m.

 

[aq1q]

i did it quickly, and i got the same answer u got in the first part. I did it another completely different way. interesting.. well i gtg.. i will try to look at this problem later.. but i don't think its right to assume the book is wrong.

 

[hage567]

They've taken the square root. I don't know why.

 

[XJellieBX]

That would work if the electrostatic force was used, but I can't see how that fits.