What is the ground state energy of an electron? I thought i did this right

[mr_coffee]

What is the ground state energy of the following.
(a) an electron

Well the formula is:
E_n = (h^2/(8*m*L^2))*n^2;
The ground state means, n = 1, its the lowest enegery level possible.
So i plugged in n = 1,
mass of e = 9.11E-31;
h = 4.136E-15 eVs;
L = 100 pm, because the book says that's tabout the size of a typical atom.
I ended up getting:
E_1 = 2.347E20 eV which was wrong, any ideas why? They really don't tell me what value i should give L, so I'm guessing that's where i screwed up maybe? In the book it says the electron is in an infintie well. thanks!

 

[Pengwuino]

You can't use the eV*s version of Planck's constant if you are using the mass in kg. You must use h=6.6261*10^-34 J*s or switch the mass to the MeV/c^2 unit and use hc = 1239.8ev*nm

 

[nrqed]

What is the ground state energy of the following.
(a) an electron

Well the formula is:
E_n = (h^2/(8*m*L^2))*n^2;
The ground state means, n = 1, its the lowest enegery level possible.
So i plugged in n = 1,
mass of e = 9.11E-31;
h = 4.136E-15 eVs;
L = 100 pm, because the book says that's tabout the size of a typical atom.
I ended up getting:
E_1 = 2.347E20 eV which was wrong, any ideas why? They really don't tell me what value i should give L, so I'm guessing that's where i screwed up maybe? thanks!

because you are mixing units... If you use eV for energy and kg for mass, you are in trouble. If you write the unit sout, you will see that tey don't simplify. My suggestion is, when you are not sure, to put everything in SI units and convert back to eV at the very end

 

[mr_coffee]

Thanks for the responce guys, when i just use the units to see what i end up with, I'm getting (J*s)^2/(kg*m^2), now if i want this in eV, 1 eV = 1.602E-19J;
but it still doesn't work out to the right units... anyone see what I'm not getting?