Solving for E(0) in Equation: Vacuum Permittivity

[FatCat0]

I cannot for the life of me figure out what value my professor used for E(0) in this equation (vacuum permittivity). Here's what he wrote down:

http://img38.imageshack.us/img38/5663/78976562.jpg

It's talking about the first ionization energy of an electron, so I've tried using numbers I do know to find a value for E(0)/e^2 (because I'm not entirely sure on the numerical value of e either, though it doesn't matter too much because the only time I need to use this constant it's in the form E(0)/e^2).

If anyone could help out, all I need is a number value to about 4 places.

 

[Bob S]

Hello FatCat-
All of the constants you need can be found at:
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-phys-constants.pdf
This includes the electron charge, the permittivity of free space, and the classical Bohr radius, all to about 6 places. The number, 13.60569172 eV, is the Rydberg energy, also on this page. pi is about 22/7.
Bob S

 

[jtbell]

I cannot for the life of me figure out what value my professor used for E(0) in this equation (vacuum permittivity).

Did you try a Google search on "vacuum permittivity"? The first hit is a Wikipedia page which gives the value in two different sets of units near the beginning.

 

[FatCat0]

I can and have looked up the constants, but I still can't find any combination of them that makes sense, either in units or in outcome. Using 8.854*10^-12 for E(0) I get this:
http://www.wolframalpha.com/input/?i=%28.511*%281.6022*10^-19%29^4%29%2F%28%284*pi*%288.854*10^-12%29%29^2*2*%286.58212*10^-22%29^2%29
Which is very clearly nowhere near...well, anything that makes sense.

 

[FatCat0]

Oh, that answer comes out to 3.13926*^-14 by the way. Copied and pasted badly there...

 

[Bob S]

Hi Fatcat-

The answer you get is in units of Joules

E = e²/8 pi ε₀ a₀ = 2.18 x 10^-18 Joules

using 1.6 x 10^-19 Joules = 1 eV (electron volt)

we get E = 13.6 eV

Bob S