Potential energy of a helium atom

[Taryn]

Consider the helium atom which consists of two electrons orbiting a nucleus made up of two protons and two neutrons. If both electrons are at a distance of r = 3.1 × 10-11 m away from the nucleus, as in figure, what is the potential energy (in eV) of the helium atom? Treat the nucleus as pointlike. - Give answer to 4 significant figures.

Okay so here is my problem... but I can't seem to get the right answer... I keep gettin a number that 10E7 higher than the answer that its meant to be... I don't really know why?
I am using the formula P.E=kqq'/r
but it just aint workin... anyone know any good formulas that may help... I got an explanation from someone but it didnt help at all! Could anyone explain it easier?

 

[dav2008]

Could you show your work so we could see where you went wrong?

Also include the given answer in the book.

 

[Taryn]

yeah no worries...
okay so wat i wrote was
u=kqq'/r
I sed that k=9E9, both q and q' are equal to 1.6E-19, coz the charge of an electron and a proton is -1.6E-19C and 1.6E-19 respectively. Btw I sed that r was 4.5 × 10-11, (from previous question that I do have the answer for)
From this I got that the first energy between the electron and the helium atom is U=9E9*-1.6E-19*(1.6E-19*2)/4.5E-11 which is about -1.024E-17... there are goin to be two of the same energies acting on the helium atom so I times this by 2... then I just put it into eV by dividing by 1.6E-19.
I got that the answer was 128 but the answer is actually meant to be
-112.5eV so I am stumped, I have tried absolutely every way... but I don't seem to be understanding wat is goin on! Its probably some stupid mistake or something I am missin, but hopefully you can help!

 

[big man]

Well really I guess we'd need to see the figure to see the orientation of the electrons, but even so I can just suggest that you need to consider the work that would be required to bring the one electron from infinity to its position near the second electron (which is your potential energy). This is given by the equation you gave of U = Kq1q2/r = ke^2/r, where r is the distance between the two electrons. The potential energy of this is then added to your original result to obtain the overall potential energy of the helium atom.
Remeber that your original result is -128 eV as well.

 

[Taryn]

helium diagram attachment

k so here is the figure, hope you can help to show me where I went wrong

 

[big man]

Well like I said previously, you'd have to take into account the potential energy of the electron being a distance r from the other electron in the atom.
I said that the diagram would be needed to see the arrangement of the electrons and from that you can see the distance they are from one another.
But if you're still having trouble then I will reply again as soon as the attachment is approved.

 

[Taryn]

Yeah I understand that but I am not sure wat that means in terms of wat I am doing wrong, I think I will try and get some help from some other class mates as well, we are all kinda tryin to work through it together, no big problem! Thanks for your help!

 

[loom91]

How would this problem have a fixed answer? Even if we use the Bohr model and treat electrons as point particles, they would not have a constant relative position so how would their potential energy contributions be calculated?

 

[Gokul43201]

I'll have to see the figure first but until then :

1. Why use a different value of r than the one provided in the question ?

2. Write down all the different 2-body PE terms for the system of 3 particles (He-atom = 1 nucleus + 2 electrons).

3. In the OP, you said you were off by an factor of 10^7, but in a subsequent post you seem to be off by only about 15%. I can understand the latter but not the former.

4. Have you covered screening and/or effective nuclear charge in class yet ? Have you come across the Slater rules ?

5. What you've calculated is the PE of 2 isolated H-atoms. Do you see how that is different from a single He-atom ?

Edit : The aqttachment is now visible. This is very bizarre, but I get the "right answer" (-112eV) using r=4.5*10^-11, though I see no good reason for using that number.