Distance between 2 charged protons (i'm desperate)

[bbhh]

I'm sure this is so easy and just 1 step. I can do questions like this, I just don't understand, this theory one, or whatever it is.

Homework Statement

How far apart are two protons if they repel each other with a force of 1.0 mN?

Homework Equations

F=k * Q1Q2/r^2

k=9.00*10^9
e=1.6*10^-19

The Attempt at a Solution

F=k * Q1Q2/r^2
.001N = 9*10^9 * 1.6*10^-19 * 1.6*10^-19/ r^2
.001 = 2.304 *10^28/r^2
r^2= 2.304*10^28/.001

r= 4.8 * 10^-13 m.***the answer key says: 1.5 x 10-11 m.

please if you could help me quick it would be amazing.

 

[rl.bhat]

Your calculation is correct.

 

[bbhh]

sorry i think i was confusing. i got 4.8 * 10^-13 m. the answer key says 1.5*10^-11. are you telling me the answer key is wrong?

 

[noblegas]

I'm sure this is so easy and just 1 step. I can do questions like this, I just don't understand, this theory one, or whatever it is.

Homework Statement

How far apart are two protons if they repel each other with a force of 1.0 mN?

Homework Equations

F=k * Q1Q2/r^2

k=9.00*10^9
e=1.6*10^-19

The Attempt at a Solution

F=k * Q1Q2/r^2
.001N = 9*10^9 * 1.6*10^-19 * 1.6*10^-19/ r^2
.001 = 2.304 *10^28/r^2
r^2= 2.304*10^28/.001
r= 4.8 * 10^-13 m.

the correct answer is: 1.5 x 10-11 m.

please if you could help me quick it would be amazing.

I think your approach and solution looks correct to me; I got the same answer. You correctly applied coulomb's Law for this case since the two protons exert an electrocstatic force on each other. Perhaps the book answer could be wrong;

 

[bbhh]

i'm doubting the answer key is wrong. there was another question that was similar in the studies (this is the review), that i also couldn't get.

 

[Feldoh]

If mN = milli-Newtons(10^-3) then you are correct in your answer of 4.8*10^-13 m.

If mN = micro-Newtons (10^-6) then you get 1.5*10^-11 m

 

[bbhh]

aahhhh.. thanks, i wasn't sure about mN and i googled it and that's what it said.

 

[Feldoh]

aahhhh.. thanks, i wasn't sure about mN and i googled it and that's what it said.

That's because m is the standard prefix for milli- (10^-3). The micro- (10^-6) prefix is usually represented with a $$\mu$$.