Quantum Electron Energy Level for Hydrogenic atom

[JewishDude]

1. Consider doubly ionized Lithium (Li++), which has one electron orbiting a +3 charge nucleus. Assuming the electron is in the ground state (n=1), what is the maximum wavelength of light, λ, that would completely ionize the Li++? (free the electron from the nucleus),
all variables and given/known data
2. Energy of a Hydrogen atom is $\frac{-13.606eV}{n^{2}}$ where 'n' is the energy level. The general formula is:
E = $\frac{-1}{4\pi r^{2}}$$\frac{me^{4}}{2\bar{h}n^{2}}$
for atoms with one electron.

For light:
E = $\frac{1240eV-nm}{λ}$
3. I assumed that Li++ would be like a hydrogen atom with 3 times the mass. Since E is proportional to m, the energy of Li should be -13.606eV*(3)/n^2 = 40.818eV. (n=1) I plugged this into the equation λ = 1240eV-nm/E, and got λ = 30.38nm.
The correct answer is 10.1nm... so I am off by a factor of three. So does this mean that the doubly ionized lithium actually has 9 times the mass?

Thank you!

 

[voko]

Mass is not the only difference between H and Li.

 

[TSny]

In the energy formula, does m stand for the mass of the atom or the mass of the electron?

 

[JewishDude]

Hi guys,
I figured it out. As it turns out m is mass of the electron, and e^4 is actually the charge of the nucleus squared times the charge of the electron squared. Which happens to be e^4 in an H atom. In this case it was e^2*(3e)^2 That's where the factor of 9 comes from! Thanks