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

Question #2476

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

Expert's answer

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= −(Z

where Z - nuclei charge. n - principal quantum number.

So, for Li

n=1. E

n=2. E

n=3. E

….....................................

n = infinity E = 0 (vacuum level)

When n=1, corresponded E = 122.4 eV – this is ionization energy for ground state.

E= −(Z

^{2}13.6[eV])/n^{2}where Z - nuclei charge. n - principal quantum number.

So, for Li

^{2+ }(Z=3) energy diagram will be something like this:n=1. E

_{1}=-122.4 eVn=2. E

_{2}=-30.6 eVn=3. E

_{3}=-13.6 eV….....................................

n = infinity E = 0 (vacuum level)

When n=1, corresponded E = 122.4 eV – this is ionization energy for ground state.

## Comments

Assignment Expert07.08.14, 17:27In 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.

Alex07.08.14, 06:17Thanks, but...

Where did the negative sign go?

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