Ionization energy of lithium atom

In summary, to estimate the ionization energy of Lithium, one can use an empirical formula found in some old textbooks for alkalis, which is a modification of Balmer's formula for Hydrogen. This formula takes into account the quantum defect and uses the Rydberg constant. For Lithium, the principal quantum number n* is known to be 1.588. However, it is not clear if this approach takes into account the electron repulsion or if it is the correct formula to use. One can also use a modification of Bohr's energy formula, which takes into account the shielding effect of inner electrons. The Bohr energy of 13.6/2^2 can be used as an approximation for the outer electron
  • #1
helpcometk
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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* ?
 
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  • #2
helpcometk said:
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
 

1. What is ionization energy?

Ionization energy is the amount of energy required to remove an electron from an atom or molecule, resulting in the formation of a positively charged ion.

2. How is ionization energy measured?

Ionization energy is typically measured in units of kilojoules per mole (kJ/mol) or electron volts (eV). It can be experimentally determined through various methods, such as spectroscopy or mass spectrometry.

3. What is the ionization energy of a lithium atom?

The ionization energy of a lithium atom is 520 kJ/mol. This means that 520 kJ of energy is required to remove one electron from a mole of lithium atoms, resulting in the formation of a Li+ ion.

4. How does ionization energy change across the periodic table?

Ionization energy generally increases from left to right across a period in the periodic table, and decreases from top to bottom within a group. This is due to the increasing nuclear charge and decreasing atomic size, which result in a stronger hold on the electrons in the outermost energy level.

5. Why does lithium have a lower ionization energy compared to other alkali metals?

Lithium has a lower ionization energy compared to other alkali metals because it has a smaller atomic radius and only has one valence electron. This makes it easier to remove the outermost electron, requiring less energy compared to other alkali metals with larger atomic radii and multiple valence electrons.

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