# Answer on Atomic and Nuclear Physics Question 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.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

Assignment Expert07.08.2014 10:27In 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.

Alex06.08.2014 23:17Thanks, but...

Where did the negative sign go?

## Leave a comment