What is the Ionization Energy of Lithium?

[helpcometk]

Homework Statement

Estimate the ionization energy of Lithium. Neglect the repulsion between
the electrons.

Homework Equations

what is the equation that can be used here? There are thousands of tables in the web having tabulated the values of various ionaziation energies.
But one can hardly find in some textbook or everywhere else a formula to calculate the ionaziation energies of atoms other than the hydrogen.
Bohr's formula vannot be used of course.

In some old textbooks dealing with atomic phenomena the following empirical formula for alkalis can be found:

En= -hcR(1/[n-δ(n,l)]²) $

where δ(n,l) is the quantum defect


or En= -hcR/n*² $$

where n* is the principal quantum number

for Li n* is given in some textbook to be 1.588

For instance we know that the ionazation energy of lithium is 5.3913 ev .


Equation $ is a modification of balmer's formula for Hydrogen.and it refers to an electron entirely outside the core.
also δ(l) is practically independent of n for a given l.

δ(l) can be found for alkalis here : Kuhn's Atomic spectra table 15(a) but since n* is known we don't need δ(l).

R is the Rydber contant.



3. The Attempt at a Solution [/b]


However I am not sure if this approach is correct ,maybe it does take into account a positive value which is added to the negative energy as a vorrection for the electron repulsion.Needless to say bohr's model is still insatisfactory with the correction for the electron repulsion.
Also if we suppose this formula is correct how do we use it to find the ionazation energy ? maybe just snbstitute n* ?

 

[ehild]

Also if we suppose this formula is correct how do we use it to find the ionazation energy ? maybe just snbstitute n* ?

The energy of a free electron is at least zero, while the bound electron has negative energy. You need to add the ionization energy to the electron to get it free.

I think you can use some of the modification of Bohr's energy formula. For a single electron around a nucleus of z charge it is En=13.6 eV (z^2/n^2). If there are more electrons the inner ones shield the nucleus on some extent. For the outer electron of lithium, the inner electrons on the closed n=1 shell are far enough to shield the nucleus and to feel only a single positive charge. So the Bohr energy 13.6/2^2 is not too bad approximation. Of course, n*=1.588 is the real one, but it is an empirical value.


ehild