Answer to Question #2476 in Atomic and Nuclear Physics for berkan

Question

Calculate the ionization energy of doubly ionized Lithium, which has Z=3. Construct also the energy level diagram for it

Answer 1

Doubly-ionized lithium is hydrogen-like atom. Atomic ionization energy can be predicted by an analysis using electrostatic potential and the Bohr model of the atom. For this model ionization energy will be:
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.