1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Quantum Electron Energy Level for Hydrogenic atom

  1. Jul 4, 2013 #1
    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 [itex]\frac{-13.606eV}{n^{2}}[/itex] where 'n' is the energy level. The general formula is:
    E = [itex]\frac{-1}{4\pi r^{2}}[/itex][itex]\frac{me^{4}}{2\bar{h}n^{2}}[/itex]
    for atoms with one electron.

    For light:
    E = [itex]\frac{1240eV-nm}{λ}[/itex]

    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!
    Last edited: Jul 4, 2013
  2. jcsd
  3. Jul 4, 2013 #2
    Mass is not the only difference between H and Li.
  4. Jul 4, 2013 #3


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    In the energy formula, does m stand for the mass of the atom or the mass of the electron?
  5. Jul 4, 2013 #4
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted