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A Conversation About Ionization Energy

 

Chlorine: Have you seen the ranking of first ionization energy of atoms?

Fluorine: I am excited to see that and know what I have done!

Cesium: Me too, Iím a big boy and I want to see my achievements.

Fluorine: Dude, I donít want to disappoint you but based on the periodic trends, you donít have a chance!

Cesium: At least, based on those periodic trends, I should be better than francium.

Francium: Oh pal, sorry, but due to relativistic effects, my first ionization energy is higher than yours.

Cesium: Wait, What? I canít tolerate this; I want to commit suicide, where do you see water?

 

Yes, thatís true!, as we can see in the above conversation, in despite of periodic trends, the first ionization energy of francium is higher than that of cesium which is attributed to the relativistic effects. The first ionization energies of cesium and francium are respectively 3.89 eV and 4.07 eV.

 

Based on general periodic trends, the first ionization energy of atoms generally increases from left to right in the periods of the common periodic table and decreases from top to bottom in its groups. The general increase of the first ionization energy from left to right in the periods is attributed to general increase of effective nuclear charge and general decrease of atomic radius across periods and the general decrease of the first ionization energy from top to bottom in groups is attributed to general increase of atomic radius across groups as a result of increase in the number of electron shells. However, none of such periodic trends are without exceptions due to different reasons. One example is the comparison between the first ionization energies of cesium and francium where cesium and francium belong to the same alkali metal group but they are in different periods: cesium is in the period 6 and francium is in the period 7. Based on the general periodic trends, francium located lower in the group than cesium should have lower first ionization energy but due to relativistic effects, we have an exception to general periodic trends in here and the first energy ionization of francium is actually higher than that of cesium.

 

But what are relativistic effects? IUPAC (in its famous gold book) considers relativistic effects as corrections to exact non-relativistic energy from the fact that inner shell electrons in heavy atoms move with velocities comparable in order of magnitude to the velocity of light. The fact is that the SchrŲdinger equation generally used to analyze quantum systems like atoms doesnít consider the theory of relativity developed by Albert Einstein. Most of time, this isnít problematic since in simple words, there is no need to consider theory of relativity at speeds much lower than the speed of light which is the case for many quantum systems. In other words, we get a same analysis with or without consideration of theory of relativity in the cases with speeds much lower than the speed of light. However, analyses with and without consideration of theory of relativity (relativistic and non-relativistic analyses) deviate from each other as the speeds of particles present in quantum systems increase and get closer to the speed of light. Such deviation increases by increase of speed and for velocities comparable in order of magnitude to the velocity of light, deviation isnít negligible and one should consider the theory of relativity to obtain the true analysis of examined system. For small but yet not negligible deviations, it is usually possible to correct non-relativistic analysis by a term or correction to get it close enough to the relativistic analysis where such corrections are generally mentioned as relativistic effects. In the case of great deviations, it is usually necessary to consider the theory of relativity from the beginning as non-relativistic analyses may completely get wrong and simple corrections maynít compensate.

 

In the case of atoms, inner shell electrons in heavy atoms move with velocities comparable in order of magnitude to the velocity of light and therefore we need to consider relativistic effects for them. In such cases, beside inner shell electrons, relativistic effects can affect outer shell electrons too since changes in states of inner shell electrons can result in changes in states of outer shell electrons beside the fact that outer shell electrons can also act as inner electrons partially as a result of their penetration to the space close to the atomic nucleus. For example, analyses show that as a result of relativistic effects, the outermost electrons of cesium and francium atoms (respectively 6s and 7s electrons) get more stable where increase in stability for the 7s electron of francium is much higher than that of 6s electron of cesium since francium is heavier than cesium (relativistic effects generally get stronger as atom gets heavier, or in fact as atomic number increases). Such changes in stabilities and energy levels affect atomic properties like the first ionization energy, e.g. the first ionization energy of francium is higher than that of cesium due to the relativistic effects. It may be interesting to know that color of gold metal is also attributed to relativistic effects. Most metals are silvery or gray however gold is yellow. Relativistic effects cause energy levels of 6s and 5d orbitals of gold get closer to each other in the way that their difference moves from the ultraviolet region of electromagnetic spectrum to the visible region. This increases absorption of blue light by gold and gold appears yellow, the complementary color to blue.

 

 

 

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