Answer to Question #2476 in Atomic and Nuclear Physics for berkan
E= −(Z2 13.6[eV])/n2
where Z - nuclei charge. n - principal quantum number.
So, for Li2+ (Z=3) energy diagram will be something like this:
n=1. E1=-122.4 eV
n=2. E2=-30.6 eV
n=3. E3=-13.6 eV
n = infinity E = 0 (vacuum level)
When n=1, corresponded E = 122.4 eV – this is ionization energy for ground state.
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In the formula for energy of the given level one assumes that energy on infinity equals 0. It is preferable for atom to have electron near the nucleus, not on infinity, so energy of such a state should be lower than for state with nucleus and electron spread on infinity. Thus, it should be negative.
Where did the negative sign go?