Doubly-ionized Lithium (Li2+) is a single-electron element, like hydrogen, but L

Question

Doubly-ionized Lithium (Li2+) is a single-electron element, like hydrogen, but Li2+ has an ionization energy of 122.4eV.Light directed at Li2+ can create ions (free electrons) if the electrons gain enough energy to escape the  atom. if you want to free electrons with a blue laser of wavelebgth landa=472nm, in what initinal energy level, n, do they need to be?

1eV = 1.602 X 10^-19J (convertion)

also note, the energy level of an electron is denoted by quantum number, n, where n=1 is the ground state.

please show all your work. thanks.

Explanation / Answer

photon energy, E=hc/lambda=h*3*10^8/472*10^-9= 4.214*10^-19 = 2.634 eV

now we know for an atom with Z atomic number, E=13.6*(Z-1)^2/n^2

=>2.634=13.6*4/n^2

=>n=4.5 so 4th energy level!

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