Ionization Energy Help
Hello everyone, this is my first time posting here so apologies if this is not the appropriate place to put this. I was going through exam review and found a question that is tripping me up. It is probably a pretty simple solution and I just can't see it because I've been looking at it too long. Here it is:
In the Bohr model of the hydrogen atom, what is the smallest amount of work that must be done on the electron to move it from its circular orbit , with a radius of 0.529x10^10m, to an infinite distance from the proton? This value is referred to as the ionization energy of hydrogen.
Here is where I am:
I used the relationship between centripetal and electrostatic force to find the velocity of the electron (2,185,309ish m/s).
Work=(Kf+Uf)(Ki+Ui), but because the electron is being moved to an infinite distance away both final energy values=0, so W=0(Ki+Ui).
I treat Ui as =kq²/r, since U=Vq and V=kq/r. K is straightforward enough
Combining all this, I end up at W=0((mv²/2)+(kq²/r)). However, the solution to the problem shows that kq²/r should be negative in this case, ie W=0((mv²/2)+(kq²/r)). The ladder solution is correct, as it comes out to 2.18x10^18J.
So my question is, why is kq²/r negative there? Again it is probably really simple, but for the life of me I can't seem to make sense of it. Any explanation would be appreciated. Thanks!
