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# The “size” of the atom in Rutherford’s model is about $1.0 \times 10^{-10} \mathrm{m} .$ (a) Determine the attractive electrostatic force between an electron and a proton separated by this distance. (b) Determine (in eV) the electrostatic potential energy of the atom.

## a) $2.3 \times 10^{-8} \, \rm N$b) $-14.4 \, \rm eV$

Atomic Physics

Nuclear Physics

### Discussion

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##### Andy C.

University of Michigan - Ann Arbor

LB
##### Aspen F.

University of Sheffield

### Video Transcript

in question. A. We have to calculate what's the attractive force between an electron and a protein that are separated by a distance off R equals 2 10 the minus stand meters. Okay. Eso The magnitude of the force is given by columns Law, which is says that the magnitude of the force f is k times the charge of the elected time to charge that problem, which is the same as a chart of the election, but with a negative sign. But since we're only working with the magnitude here, I'm not gonna take the The sign into account divided by R square Que is nine about nine time since the nine Newtons meters squared. Rick, whom spare times is where which is 1.6 times 10 to the minus 19th booms squared, divided by R square, which is 10 to the minus 10 meters square. So the force is equal to two points three times 10 to the minus eight Newtons. Okay, this is the force and in question be we have to calculate the electric static potential energy in the atom and we know that the energy is equal to K times the charge of the electorate, which is minor z times the charge of a protein which is just yeah, divided by And okay, so this year will be minus K, which is nine times 10 to the ninth is before Newtons meters squared, Makumbe Square times e and I'm gonna do like this I'm gonna multiply one by one e So it's ah, 1.6 times 10 to the minus 19. Coombs, I'm gonna leave out the other E because I want the answering electing votes. Okay, so I'm just, uh, separating here. The charge of the election divided by R, which is 10 to the minus 10 meters, and the answer is minus 14.4 votes times the charge of the election. So this is minus 14.4 electoral votes. And this is the answer to the second question.

#### Topics

Atomic Physics

Nuclear Physics

##### Andy C.

University of Michigan - Ann Arbor

LB
##### Aspen F.

University of Sheffield