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Ionization Energy and Charge Shielding of Electrons in Atoms and Ions (Part II)
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Ionization Energy and Charge<�br>
Shielding of Electrons <�br>
in Atoms and Ions (Part II)<�/b><�/FONT><�/CENTER>
<�/th><�/TABLE> <�/CENTER>
<�b><�p>
<�p>This is a continuation of a study on the ionization energy for electrons in different positions within
atoms and ions. Ionization energy IE, or as it is usually called <�i>the ionization potential<�/i>, for an electron
is the amount of energy required to dislodge it. The previous <�a href="chargeshielding.htm">study<�/a>
was limited to only five cases for each electron position. The more extensive database is displayed in the
appendix.
<�h2>Ionization Energies<�/h2>
<�p>The Bohr model of a hydrogen-like atom or ion
indicates that the energy required to remove an electron, called the ionization
potential, should follow the formula
<�h4>
IE = RZ²/n²
<�/h4>
<�p>where R is the Rydberg constant (approximately 13.6 electron Volts (eV), Z is the net charge experienced by the electron and n is
the principal quantum number, effectively the shell number.
<�p>Here are the graphs of the ionization potential of the three innermost electrons.
<�p><�center><�img src="chargeshielding2a.gif"><�/center>
<�p><�center><�img src="chargeshielding2b.gif"><�/center>
<�p><�center><�img src="chargeshielding2c.gif"><�/center>
<�p>Clearly the relationships are very regular and quadratic. The graph for the first electron exhibits an unexplained jump in
ionization energy after ten protons. The data for none of the other electron positions exhibit such a jump.
<�p>Let p denote the number of protons in the nucleus of the atom or ion.
The value of Z in the above Bohr formula is the number of protons in the nucleus p less the
shielding ε by the electrons in inner shells or in the same shell.
Thus the ionization energy would be
<�h4>
IE = (R/n²)(p−ε)²
<�br>which can be put in the form<�br>
IE = (R/n²)(p² − 2pε + ε²)
<�/h4>
<�p>There may be other phenomena that affect the ionization energy besides
the charge of the nucleus and the shielding. For example there may be
energy associated with the spin pairing of electrons. Thus the formula should
be
<�h4>
IE = (R/n²)p² − 2(R/n²)εp + ζ
<�/h4>
<�p>where the ζ term includes the ε² term and any other factors
affecting ionization energy.
<�p>
<�h2>Charge Shielding<�/h2>
<�p>The Bohr model is strictly for a hydrogen-like atom or ion; i.e., one in which there is a single electron in the outermost
shell. However the regression equation also fits very well the cases of multiple electrons in the outer shells if charge shielding
is taken into account. That shielding is by the electrons in the inner shells and may also be by electrons in the same shell.
But the shielding by electrons in the same
shell is likely only for a fraction of their charge. As it turns out, shielding even for electrons in the inner shells the shielding is less than the
full value of their charges.
<�p>Here is the rationale for the shieldings. If inner shell electrons
execute trajectories that take them over a spherical shell it is as though their charges are
smeared over a spherical shell and their effect on outer shell electrons is the same as
though the charges of the inner shell electrons are concentrated at the center of the atom or ion
and thus cancel out an equal number of positive charges.
<�p> The electrons in a lower subshell
may be entirely interior to an outer subshell. Thus the analysis should be
in terms of shielding by electrons in inner shells and subshells versus shielding
by electrons in the same subshell.
<�p>The shielding by electrons in the same subshell is a bit more complicated. The effect of
a charge distributed over a spherical shell on an electron entirely within that spherical shell
is zero. If the electron is entirely outside of the spherical shell the effect is the same as
if the charge were concentrated at the center of the spherical shell. But if the center of the
electron is located exactly on the shell then roughly half of the electron is inside of the
spherical shell and is unaffected by its charge. Thus an electron is shielded by an amount
approximately equal to one half of the charges in the same shell. That is the rough theory. It needs
to be tested empirically.
<�p>This partial shielding by electrons in the same shell explains how there can be negative ions.
In a negative ion such as O<�sup>=<�/sup>
there are outer electrons clinging to a structure with overall negative charge. That appears to be a puzzle.
The oxygen nucleus has eight protons. There
are two electrons in the first shell and six in the second shell of the oxygen atom. Overall that is electrostatically neutral.
But for a seventh electron in the second shell the two electrons in the inner shell and other six electrons in the second shell
shield only a portion of the positive charge of the nucleus. Thus there is a positive attraction for that seventh electron. And
since the seventh electron shields only a fraction of a unit charge for the eighth there is a positive attraction for the
eighth electron. However another electron would go into a third shell and the ten (2+8) other electrons would be inner shell
electrons and could more than shield the eight positive charges of the nucleus. Thus there would be a repulsion of an eleventh
electron.
<�h2>Empirical Analysis<�/h2>
<�p>The extended Bohr formula for ionization energy suggests a regression equation of the form
<�h4>
IE = c<�sub>2<�/sub>p² + c<�sub>1<�/sub>p + c<�sub>0<�/sub>
<�/h4>
<�p>Such a form does give a very good fit to the data.
The value of ε can be found from the regression coefficients as
<�h4>
ε = −½c<�sub>1<�/sub>/c<�sub>2<�/sub>
<�/h4>
<�p>For the second electron the quadratic regression that fits the data is
<�h4>
IE = 13.72673p² − 18.61822p + 8.80897<�br>
[1607.6]
[-96.8] [9.5]
<�/h4>
<�p>Note that the Rydberg constant is 13.60569 eV.
<�p>The coefficient of determination for this equation is 0.999999673
and the standard error of the estimate is 0.9945 eV.
<�p>The figures in square brackets are the t-ratios for the regression coefficients
1above them; i.e., the ratios of the regression coefficients to their standard deviations.
`A t-ratio of less than 2 would indicate that at the 95 percent degree of confidence
the perceived relationship between the independent variable for the coefficient and
the dependent variable is not real; i.e., is just due to chance. The t-ratios for
the above regression equation are astronomically high.
<�!--
13.7267308 -18.61822492 8.808965738
0.008538505 0.192410252 0.930454222
0.999999673 0.994506819 #N/A
24430807.54 16 #N/A
48326278.12 15.82470102 #N/A 0,678174
1607.626874 -96.76316499 9.467382196
-->
<�p>The estimate of ε which comes from this equation
<�h4>
ε = −½(-18.61822)/13.72673 = 0.67817 electron charges.
<�/h4>
<�p>Thus the shielding by another electron in the same shell is real and is approximately 0.5 electron charges.
<�p>The s-subshell of the second shell can contain at most two electrons. Therefore
the third and fourth electrons are in that subshell. The "expected" shieldings for the
third and fourth electrons are 2.0 and 2.5, respectively. This expectation is in the
nature of "naively expected."
<�p>For the third electron (the first in the second shell) the regression equation is
<�h4>
IE = 3.43641p² − 11.32175p + 8.60728
<�br>
[2472.7]
[-347.3] [51.5]
<�/h4>
<�!--
3.436412926 -11.32175426 8.607283282 1.647321568
0.001389725 0.032601808 0.167291148
0.999999872 0.141287919 #N/A
58703076.28 15 #N/A
2343694.028 0.299434141 #N/A
2472.729247 -347.2738138 51.45091886
-->
<�p>The coefficient of determination for this equation is 0.999999872
and the standard error of the estimate is 0.14129 eV.
<�p>The estimate of ε which comes from this equation
<�h4>
ε = −½(-11.32175)/3.436413 = 1.64732 electron charges.
<�/h4>
<�p>Full shielding by the two electrons in the first shell would give ε=2.0.
<�p>The coefficient of p² is R/n² where n for the second shell is 2.
Thus the R value for this case is 2²(3.436413)=13.7456517, close to the
Rydberg constant of 13.60569 eV.
<�p>The fifth through tenth
electrons are in the p-subshell of the second shell. Therefore their "expected" shieldings
are 4.0, 4.5, 5.0, 5.5, 6.0 and 6.5, respectively. The shielding values found for the fifth
through eighth electrons are
3.16858, 3.82658, 4.52719
and 5.31449.
Thus there is a close match for the eighth
electron. The measured shielding for the
ninth electron is 5.99813, reasonably close to 6.0.
<�p>The measured shielding for the
tenth electron is
6.81818, surprisingly exceeding the "expected" value 6.5.
<�p>Now it is worthwhile to apply the above methodology to the case of the first electron.
There is no shielding in this case so ε should be zero. But it should not be applied
to interval that includes the jump.
<�p>The regression equation for the first electron for p=1 through p=11 is
<�h4>
IE = 13.64589p² − 0.27454p + 0.36410<�br>
[3434.8]
[-5.6] [2.8]
<�/h4>
<�!--
e=0
13.64588695 -0.274543357 0.36409697 0.010059564
0.003972855 0.048948413 0.127800025
0.999999965 0.116371431 #N/A
114436026 8 #N/A
3099456.258 0.108338479 #N/A
3434.780896 -5.608830597 2.848958508
-->
<�p>The coefficient of determination for this equation is 0.999999965
and the standard error of the estimate is 0.11637 eV.
<�p>The estimate of ε which comes from this equation is 0.01006 charges.
This is essentially zero, thus confirming the methodology.
<�p>The eleventh electron is in the third shell. There are ten electrons in the first
two shells so the shielding would be expected to be 10.0. Its measured value
is 8.17159, about 0.8 of its "expected" value.
<�p>The measured value of the shielding for the twelfth electron
is 8.17159, about 0.8 of its "expected" value.
8.78703 charges, 0.61544 charges higher than the value for the eleventh electron.
<�p>The table of the above values and the values for subsequent electron positions is:
<�p><�CENTER>
<�TABLE cellPadding=20 bgColor=#ffff00 border=9 frame=box>
<�th colspan=5>Shielding of Electrons in Different Positions in Atoms
and Ions<�/th>
<�tr><�td>Electron<�br>Position <�/td><�td>Inner<�br>Electrons<�/td>
<�td>Same<�br>Shell<�br>Electrons<�/td><�td>Shielding<�/td><�td>"Expected"<�br>Shielding<�/td><�/tr>
<�tr><�td>1<�/td><�td>0<�/td><�td>0<�/td><�td>0.010<�/td><�td>0.000<�/td><�/tr>
<�tr><�td>2<�/td><�td>0<�/td><�td>1<�/td><�td>0.678<�/td><�td>0.500<�/td><�/tr>
<�tr><�td>3<�/td><�td>2<�/td><�td>0<�/td><�td>1.647<�/td><�td>2.00<�/td><�/tr>
<�tr><�td>4<�/td><�td>2<�/td><�td>1<�/td><�td>2.221<�/td><�td>2.500<�/td><�/tr>
<�tr><�td>5<�/td><�td>4<�/td><�td>0<�/td><�td>3.169<�/td><�td>4.00<�/td><�/tr>
<�tr><�td>6<�/td><�td>4<�/td><�td>1<�/td><�td>3.827<�/td><�td>4.500<�/td><�/tr>
<�tr><�td>7<�/td><�td>4<�/td><�td>2<�/td><�td>4.527<�/td><�td>5.000<�/td><�/tr>
<�tr><�td>8<�/td><�td>4<�/td><�td>3<�/td><�td>5.314<�/td><�td>5.500<�/td><�/tr>
<�tr><�td>9<�/td><�td>4<�/td><�td>4<�/td><�td>5.998<�/td><�td>6.000<�/td><�/tr>
<�tr><�td>10<�/td><�td>4<�/td><�td>5<�/td><�td>6.818<�/td><�td>6.500<�/td><�/tr>
<�tr><�td>11<�/td><�td>10<�/td><�td>0<�/td><�td>8.17159<�/td><�td>10.000<�/td><�/tr>
<�tr><�td>12<�/td><�td>10<�/td><�td>1<�/td><�td>8.78703<�/td><�td>10.500<�/td><�/tr>
<�tr><�td>13<�/td><�td>10<�/td><�td>2<�/td><�td>10.13256<�/td><�td>11.000<�/td><�/tr>
<�tr><�td>14<�/td><�td>10<�/td><�td>3<�/td><�td>10.61864<�/td><�td>11.500<�/td><�/tr>
<�tr><�td>15<�/td><�td>10<�/td><�td>4<�/td><�td>11.26194<�/td><�td>12.000<�/td><�/tr>
<�tr><�td>16<�/td><�td>10<�/td><�td>5<�/td><�td>12.01621<�/td><�td>12.5<�/td><�/tr>
<�tr><�td>17<�/td><�td>10<�/td><�td>6<�/td><�td>12.68347<�/td><�td>13.0<�/td><�/tr>
<�tr><�td>18<�/td><�td>10<�/td><�td>7<�/td><�td>13.33016<�/td><�td>13.500<�/td><�/tr>
<�tr><�td>19<�/td><�td>18<�/td><�td>0<�/td><�td>16.45756<�/td><�td>18.000<�/td><�/tr>
<�tr><�td>20<�/td><�td>18<�/td><�td>1<�/td><�td>17.37618<�/td><�td>18.500<�/td><�/tr>
<�tr><�td><�/td><�td><�/td><�td><�/td><�td><�/td><�td><�/td><�/tr>
<�/table><�/center>
<�p>Before proceeding further it is necessary to note a feature of the electron
structure of atoms beyond Argon (p=18). The 19th electron goes into
the s-subshell of the fourth electronic shell even though there is additional
capacity in the d-subshell of the third shell. It does this because of energy
considerations.
<�p>The 20th electron also goes into
the s-subshell of the fourth shell but subsequent electrons go into the
d-subshell of the third shell. This creates a problem of the identification
of the data for the 21st through the 30th electron. Apparently this is
for the outermost electron. For the cases of 21 through 28 there are
two electrons in the s-subshell of the fourth shell. Cu (p=29) is the
anomaly it has only one electron in the s-subshell of the fourth shell.
Zn (p=30) again has two electrons in the s-subshell of the fourth shell.
<�p><�CENTER>
<�TABLE cellPadding=20 bgColor=#ffdd00 border=9 frame=box>
<�th colspan=5>Shielding of Electrons in Different Positions in Atoms
and Ions<�/th>
<�tr><�td>Electron<�br>Position <�/td><�td>Inner<�br>Electrons<�/td>
<�td>Same<�br>Shell<�br>Electrons<�/td><�td>Shielding<�/td><�td>"Expected"<�br>Shielding<�/td><�/tr>
<�tr><�td>21<�/td><�td>19<�/td><�td>1<�/td><�td>18.33305<�/td><�td>19.500<�/td><�/tr>
<�tr><�td>22<�/td><�td>20<�/td><�td>1<�/td><�td>19.32662<�/td><�td>20.500<�/td><�/tr>
<�tr><�td>23<�/td><�td>21<�/td><�td>1<�/td><�td>20.23488<�/td><�td>21.500<�/td><�/tr>
<�tr><�td>24<�/td><�td>22<�/td><�td>1<�/td><�td>21.99433<�/td><�td>22.500<�/td><�/tr>
<�tr><�td>25<�/td><�td>23<�/td><�td>1<�/td><�td>23.01113<�/td><�td>23.500<�/td><�/tr>
<�tr><�td>26<�/td><�td>24<�/td><�td>1<�/td><�td>24.57486<�/td><�td>24.500<�/td><�/tr>
<�tr><�td>27<�/td><�td>25<�/td><�td>1<�/td><�td>25.67367<�/td><�td>25.500<�/td><�/tr>
<�tr><�td>28<�/td><�td>26<�/td><�td>1<�/td><�td>23.49360<�/td><�td>26.500<�/td><�/tr>
<�tr><�td>29<�/td><�td>28<�/td><�td>0<�/td><�td>24.05092<�/td><�td>28.000<�/td><�/tr>
<�tr><�td>30<�/td><�td>28<�/td><�td>1<�/td><�td>25.17227<�/td><�td>28.500<�/td><�/tr>
<�tr><�td><�/td><�td><�/td><�td><�/td><�td><�/td><�td><�/td><�/tr>
<�/table><�/center>
<�p><�CENTER>
<�TABLE cellPadding=20 bgColor=#ffddff border=9 frame=box>
<�th colspan=5>Shielding of Electrons in Different Positions in Atoms
and Ions<�/th>
<�tr><�td>Electron<�br>Position <�/td><�td>Inner<�br>Electrons<�/td><�td>Same<�br>Shell<�br>Electrons<�/td><�td>Shielding<�/td><�td>"Expected"<�br>Shielding<�/td><�/tr>
<�tr><�td>31<�/td><�td>30<�/td><�td>0<�/td><�td>26.5035<�/td><�td>30.000<�/td><�/tr>
<�tr><�td>32<�/td><�td>30<�/td><�td>1<�/td><�td>27.24866<�/td><�td>30.500<�/td><�/tr>
<�tr><�td>33<�/td><�td>30<�/td><�td>2<�/td><�td>28.46114<�/td><�td>31.000<�/td><�/tr>
<�tr><�td>34<�/td><�td>30<�/td><�td>3<�/td><�td>29.01879<�/td><�td>31.500<�/td><�/tr>
<�tr><�td>35<�/td><�td>30<�/td><�td>4<�/td><�td>29.98610<�/td><�td>32.000<�/td><�/tr>
<�tr><�td>36<�/td><�td>30<�/td><�td>5<�/td><�td>29.93740<�/td><�td>32.500<�/td><�/tr>
<�tr><�td>37<�/td><�td>36<�/td><�td>0<�/td><�td>34.97742<�/td><�td>36.000<�/td><�/tr>
<�tr><�td>38<�/td><�td>36<�/td><�td>1<�/td><�td>37.42557<�/td><�td>36.500<�/td><�/tr>
<�tr><�td>39<�/td><�td>37<�/td><�td>1<�/td><�td>38.69343<�/td><�td>37.500<�/td><�/tr>
<�tr><�td>40<�/td><�td>39<�/td><�td>0<�/td><�td>39.10448<�/td><�td>39.000<�/td><�/tr>
<�tr><�td><�/td><�td><�/td><�td><�/td><�td><�/td><�td><�/td><�/tr>
<�/table><�/center>
<�h2>Average Shielding Ratios<�/h2>
<�p>The "expected" shieldings of an electron based on the number of electrons in inner subshells and shells
and the number of electrons in the same subshell are not precise estimates of the measured shieldings
but are rough approximations. It might be the ratios used of 1.0 for the inner electrons and 0.5 for
the same subshell electrons are not the best ratios for predicting the shieldings.
<�p>There are forty observations in the above empirical analysis which can be used
to obtain the best ratios. Let Inner and Same be the number of the shielding electrons.
Then the regression equation presumed is
<�h4>
ε = r<�sub>I<�/sub>(Inner) + r<�sub>S<�/sub>(Same)
<�/h4>
<�p>There is no intercept constant for the equation because if there are no shielding electrons there is no shielding.
<�p>The regression results are:
<�h4>
ε = 0.94935(Inner) + 0.47607(Same)
<�br>
[92.1]
[5.6]
<�/h4>
<�!--
0.476074358 0.949349354 0
0.085308093 0.010304452 #N/A
0.996851178 1.201048312 #N/A
6015.00267 38 #N/A
17353.48778 54.81564779 #N/A
5.580647063 92.1300179 #N/A
0.553145962 0.96509676 -0.521212813
0.105294478 0.01636719 0.422748456
0.98963298 1.192912781 #N/A
1766.005067 37 #N/A
5026.194896 52.65251345 #N/A
5.253323545 58.96533013 -1.232914765
-->
<�p>Lo and behold! The ratio values of 1.0 and 0.5 are very close to the best values for predicting the shielding
of an electron. The coefficient of determination for the regression equation is 0.99685 and the standard error
of the estimate is 1,20 eV. Thus about 99.7 percent of the variation in the shielding ε is explained
by the variation in the numbers of shielding electrons.
<�p>If a constant is included in the regression the t-ratio for its estimate is −1.2, indicating the constant
is not significantly different from zero at the 95 percent level of confidence.
<�p>(To be continued.)
<�h2>Conclusions<�/h2>
<�p>The energy required to dislodge an electron from a position in an atom is determined
by the net positive charge it experiences from the nucleus. The net experienced charge
is the charge of the nucleus less the amount that it is shielded from by the electrons in
the inner shells and subshells and also by the electrons in the same subshell. The
shielding by the electrons in the same subshell is a fraction of their charge, roughly one
half. The shielding by electrons in inner shells or shells is generally less than one for one,
but roughly 0.95.
<�p>Fractional shielding accounts for the existence of negative ions.
<�HR>
<�h2>Appendix<�/h2>
<�p>This data was compiled from a database published by the Physics Department of Ohio State University.
<�p><�TABLE cellPadding=20 bgColor=#ffff00 border=9 frame=box><�th colspan=12>
<�center> Ionization Energies (eV)<�/center><�/th>
<�tr><�td> <�/td><�td> <�/td><�td colspan=10>Electron Number<�/td><�/tr>
<�tr><�td> Elem. <�/td><�td>Number of <�br>Protons <�/td><�td> 1 <�/td><�td> 2 <�/td><�td> 3 <�/td><�td> 4 <�/td><�td> 5 <�/td><�td> 6 <�/td><�td> 7 <�/td><�td> 8 <�/td><�td> 9 <�/td><�td> 10 <�/td><�/tr>
<�tr><�td> H <�/td><�td> 1 <�/td><�td> 13.598 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> He <�/td><�td> 2 <�/td><�td> 54.416 <�/td><�td> 24.587 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Li <�/td><�td> 3 <�/td><�td> 122.451 <�/td><�td> 76.638 <�/td><�td> 5.392 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Be <�/td><�td> 4 <�/td><�td> 217.713 <�/td><�td> 153.893 <�/td><�td> 18.211 <�/td><�td> 9 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> B <�/td><�td> 5 <�/td><�td> 340.217 <�/td><�td> 259.368 <�/td><�td> 37.93 <�/td><�td> 25.154 <�/td><�td> 8.298 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> C <�/td><�td> 6 <�/td><�td> 489.981 <�/td><�td> 392.077 <�/td><�td> 64.492 <�/td><�td> 47.887 <�/td><�td> 24.383 <�/td><�td> 11.26 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> N <�/td><�td> 7 <�/td><�td> 667.029 <�/td><�td> 552.057 <�/td><�td> 97.888 <�/td><�td> 77.472 <�/td><�td> 47.448 <�/td><�td> 29.601 <�/td><�td> 14.534 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> O <�/td><�td> 8 <�/td><�td> 871.387 <�/td><�td> 739.315 <�/td><�td> 138.116 <�/td><�td> 113.896 <�/td><�td> 77.412 <�/td><�td> 54.934 <�/td><�td> 35.116 <�/td><�td> 13.618 <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> F <�/td><�td> 9 <�/td><�td> 1103.089 <�/td><�td> 953.886 <�/td><�td> 185.182 <�/td><�td> 157.161 <�/td><�td> 114.24 <�/td><�td> 87.138 <�/td><�td> 62.707 <�/td><�td> 34.97 <�/td><�td> 17.422 <�/td><�td> <�/td><�/tr>
<�tr><�td> Ne <�/td><�td> 10 <�/td><�td> 1362.164 <�/td><�td> 1195.797 <�/td><�td> 239.09 <�/td><�td> 207.27 <�/td><�td> 157.93 <�/td><�td> 126.21 <�/td><�td> 97.11 <�/td><�td> 63.45 <�/td><�td> 40.962 <�/td><�td> 21.564 <�/td><�/tr>
<�tr><�td> Na <�/td><�td> 11 <�/td><�td> 1648.659 <�/td><�td> 1465.091 <�/td><�td> 299.87 <�/td><�td> 264.18 <�/td><�td> 208.47 <�/td><�td> 172.15 <�/td><�td> 128.39 <�/td><�td> 98.91 <�/td><�td> 71.64 <�/td><�td> 47.286 <�/td><�/tr>
<�tr><�td> Mg <�/td><�td> 12 <�/td><�td> 2304.08 <�/td><�td> 1761.802 <�/td><�td> 367.53 <�/td><�td> 327.95 <�/td><�td> 265.9 <�/td><�td> 224.94 <�/td><�td> 186.5 <�/td><�td> 141.26 <�/td><�td> 109.24 <�/td><�td> 80.143 <�/td><�/tr>
<�tr><�td> Al <�/td><�td> 13 <�/td><�td> 2673.108 <�/td><�td> 2085.983 <�/td><�td> 442.07 <�/td><�td> 398.57 <�/td><�td> 330.21 <�/td><�td> 284.59 <�/td><�td> 241.43 <�/td><�td> 190.47 <�/td><�td> 153.71 <�/td><�td> 119.99 <�/td><�/tr>
<�tr><�td> Si <�/td><�td> 14 <�/td><�td> 3069.762 <�/td><�td> 2437.676 <�/td><�td> 523.5 <�/td><�td> 476.06 <�/td><�td> 401.43 <�/td><�td> 351.1 <�/td><�td> 303.17 <�/td><�td> 246.52 <�/td><�td> 205.05 <�/td><�td> 166.77 <�/td><�/tr>
<�tr><�td> P <�/td><�td> 15 <�/td><�td> 3494.099 <�/td><�td> 2816.943 <�/td><�td> 611.85 <�/td><�td> 560.41 <�/td><�td> 479.57 <�/td><�td> 424.5 <�/td><�td> 371.73 <�/td><�td> 309.41 <�/td><�td> 263.22 <�/td><�td> 230.43 <�/td><�/tr>
<�tr><�td> S <�/td><�td> 16 <�/td><�td> 3946.193 <�/td><�td> 3223.836 <�/td><�td> 707.14 <�/td><�td> 651.63 <�/td><�td> 564.65 <�/td><�td> 504.78 <�/td><�td> 447.09 <�/td><�td> 379.1 <�/td><�td> 328.23 <�/td><�td> 280.93 <�/td><�/tr>
<�tr><�td> Cl <�/td><�td> 17 <�/td><�td> 4426.114 <�/td><�td> 3658.425 <�/td><�td> 809.39 <�/td><�td> 749.74 <�/td><�td> 656.69 <�/td><�td> 591.97 <�/td><�td> 529.26 <�/td><�td> 455.62 <�/td><�td> 400.05 <�/td><�td> 348.28 <�/td><�/tr>
<�tr><�td> Ar <�/td><�td> 18 <�/td><�td> 4933.931 <�/td><�td> 4120.778 <�/td><�td> 918 <�/td><�td> 854.75 <�/td><�td> 755.73 <�/td><�td> 686.09 <�/td><�td> 618.24 <�/td><�td> 538.95 <�/td><�td> 478.68 <�/td><�td> 422.44 <�/td><�/tr>
<�tr><�td> K <�/td><�td> 19 <�/td><�td> 5469.738 <�/td><�td> 4610.955 <�/td><�td> 1034 <�/td><�td> 968 <�/td><�td> 861.77 <�/td><�td> 787.13 <�/td><�td> 714.02 <�/td><�td> 629.09 <�/td><�td> 564.13 <�/td><�td> 503.44 <�/td><�/tr>
<�tr><�td> Ca <�/td><�td> 20 <�/td><�td> <�/td><�td> 5129.045 <�/td><�td> 1157 <�/td><�td> 1087 <�/td><�td> 974 <�/td><�td> 895.12 <�/td><�td> 816.61 <�/td><�td> 726.03 <�/td><�td> 656.39 <�/td><�td> 591.25 <�/td><�/tr>
<�tr><�td> Sc <�/td><�td> 21 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 926 <�/td><�td> 829.79 <�/td><�td> 755.47 <�/td><�td> 685.89 <�/td><�/tr>
<�tr><�td> Ti <�/td><�td> 22 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 940.36 <�/td><�td> 861.33 <�/td><�td> 787.33 <�/td><�/tr>
<�tr><�td> V <�/td><�td> 23 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 974.02 <�/td><�td> 895.58 <�/td><�/tr>
<�tr><�td> Cr <�/td><�td> 24 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1010.64 <�/td><�td> 1010.64 <�/td><�/tr>
<�tr><�td> Mn <�/td><�td> 25 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1136.2 <�/td><�td> 1136.2 <�/td><�/tr>
<�tr><�td> Fe <�/td><�td> 26 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1266.1 <�/td><�td> 1266.1 <�/td><�/tr>
<�tr><�td> Co <�/td><�td> 27 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1403 <�/td><�td> 1403 <�/td><�/tr>
<�tr><�td> Ni <�/td><�td> 28 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1547 <�/td><�/tr>
<�tr><�td> Cu <�/td><�td> 29 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1698 <�/td><�/tr>
<�tr><�td> Zn <�/td><�td> 30 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 1856 <�/td><�/tr>
<�/table>
<�p><�TABLE cellPadding=20 bgColor=#00ffff border=9 frame=box><�th colspan=10>
<�center> Ionization Energies (eV)<�/center><�/th>
<�tr><�td> <�/td><�td> <�/td><�td colspan=8>Electron Number<�/td><�/tr>
<�tr><�td> Elem. <�/td><�td> Number of <�br>Protons <�/td><�td> 11 <�/td><�td> 12 <�/td><�td> 13 <�/td><�td> 14 <�/td><�td> 15 <�/td><�td> 16 <�/td><�td> 17 <�/td><�td> 18 <�/td><�/tr>
<�tr><�td> Na <�/td><�td> 11 <�/td><�td> 5.139 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Mg <�/td><�td> 12 <�/td><�td> 15.035 <�/td><�td> 7.646 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Al <�/td><�td> 13 <�/td><�td> 28.447 <�/td><�td> 18.828 <�/td><�td> 5.986 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Si <�/td><�td> 14 <�/td><�td> 45.141 <�/td><�td> 33.492 <�/td><�td> 16.345 <�/td><�td> 8.151 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> P <�/td><�td> 15 <�/td><�td> 65.023 <�/td><�td> 51.37 <�/td><�td> 30.18 <�/td><�td> 19.725 <�/td><�td> 10.486 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> S <�/td><�td> 16 <�/td><�td> 88.049 <�/td><�td> 72.68 <�/td><�td> 47.3 <�/td><�td> 34.83 <�/td><�td> 23.33 <�/td><�td> 10.36 <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Cl <�/td><�td> 17 <�/td><�td> 114.193 <�/td><�td> 98.03 <�/td><�td> 67.8 <�/td><�td> 53.46 <�/td><�td> 39.61 <�/td><�td> 23.81 <�/td><�td> 12.967 <�/td><�td> <�/td><�/tr>
<�tr><�td> Ar <�/td><�td> 18 <�/td><�td> 143.456 <�/td><�td> 124.319 <�/td><�td> 91.007 <�/td><�td> 75.02 <�/td><�td> 59.81 <�/td><�td> 40.74 <�/td><�td> 27.629 <�/td><�td> 15.759 <�/td><�/tr>
<�tr><�td> K <�/td><�td> 19 <�/td><�td> 175.814 <�/td><�td> 154.86 <�/td><�td> 117.56 <�/td><�td> 100 <�/td><�td> 82.66 <�/td><�td> 60.91 <�/td><�td> 45.72 <�/td><�td> 31.625 <�/td><�/tr>
<�tr><�td> Ca <�/td><�td> 20 <�/td><�td> 211.27 <�/td><�td> 188.54 <�/td><�td> 147.24 <�/td><�td> 127.7 <�/td><�td> 108.78 <�/td><�td> 84.41 <�/td><�td> 67.1 <�/td><�td> 50.908 <�/td><�/tr>
<�tr><�td> Sc <�/td><�td> 21 <�/td><�td> 249.832 <�/td><�td> 225.32 <�/td><�td> 180.02 <�/td><�td> 158.7 <�/td><�td> 138 <�/td><�td> 111.1 <�/td><�td> 91.66 <�/td><�td> 73.47 <�/td><�/tr>
<�tr><�td> Ti <�/td><�td> 22 <�/td><�td> 291.497 <�/td><�td> 265.23 <�/td><�td> 215.91 <�/td><�td> 193.2 <�/td><�td> 168.5 <�/td><�td> 140.8 <�/td><�td> 119.36 <�/td><�td> 99.22 <�/td><�/tr>
<�tr><�td> V <�/td><�td> 23 <�/td><�td> 336.267 <�/td><�td> 308.25 <�/td><�td> 255.04 <�/td><�td> 230.5 <�/td><�td> 205.8 <�/td><�td> 173.7 <�/td><�td> 150.17 <�/td><�td> 128.12 <�/td><�/tr>
<�tr><�td> Cr <�/td><�td> 24 <�/td><�td> 384.3 <�/td><�td> 355 <�/td><�td> 298 <�/td><�td> 270.8 <�/td><�td> 244.4 <�/td><�td> 209.3 <�/td><�td> 184.7 <�/td><�td> 161.1 <�/td><�/tr>
<�tr><�td> Mn <�/td><�td> 25 <�/td><�td> 435.3 <�/td><�td> 404 <�/td><�td> 343.6 <�/td><�td> 314.4 <�/td><�td> 286 <�/td><�td> 248.3 <�/td><�td> 221.8 <�/td><�td> 196.46 <�/td><�/tr>
<�tr><�td> Fe <�/td><�td> 26 <�/td><�td> 489.5 <�/td><�td> 457 <�/td><�td> 392.2 <�/td><�td> 361 <�/td><�td> 330.8 <�/td><�td> 290.4 <�/td><�td> 262.1 <�/td><�td> 235.04 <�/td><�/tr>
<�tr><�td> Co <�/td><�td> 27 <�/td><�td> 546.8 <�/td><�td> 512 <�/td><�td> 444 <�/td><�td> 411 <�/td><�td> 379 <�/td><�td> 336 <�/td><�td> 305 <�/td><�td> 276 <�/td><�/tr>
<�tr><�td> Ni <�/td><�td> 28 <�/td><�td> 607.2 <�/td><�td> 571 <�/td><�td> 499 <�/td><�td> 464 <�/td><�td> 430 <�/td><�td> 384 <�/td><�td> 352 <�/td><�td> 321.2 <�/td><�/tr>
<�tr><�td> Cu <�/td><�td> 29 <�/td><�td> 671 <�/td><�td> 633 <�/td><�td> 557 <�/td><�td> 520 <�/td><�td> 484 <�/td><�td> 435 <�/td><�td> 401 <�/td><�td> 368.8 <�/td><�/tr>
<�tr><�td> Zn <�/td><�td> 30 <�/td><�td> 738 <�/td><�td> 698 <�/td><�td> 619 <�/td><�td> 579 <�/td><�td> 542 <�/td><�td> 490 <�/td><�td> 454 <�/td><�td> 419.7 <�/td><�/tr>
<�/table>
<�p><�TABLE cellPadding=20 bgColor=#00ff00 border=9 frame=box><�th colspan=14>
<�center> Ionization Energies (eV)<�/center><�/th>
<�tr><�td> <�/td><�td> <�/td><�td colspan=12>Electron Number<�/td><�/tr>
<�tr><�td> Elem. <�/td><�td> Number of <�br>Protons <�/td><�td> 19 <�/td><�td> 20 <�/td><�td> 21 <�/td><�td> 22 <�/td><�td> 23 <�/td><�td> 24 <�/td><�td> 25 <�/td><�td> 26 <�/td><�td>27 <�/td><�td>28 <�/td><�td>29 <�/td><�td>30<�/td><�/tr>
<�tr><�td> K <�/td><�td> 19 <�/td><�td> 4.341 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Ca <�/td><�td> 20 <�/td><�td> 11.871 <�/td><�td> 6.113 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Sc <�/td><�td> 21 <�/td><�td> 24.76 <�/td><�td> 12.8 <�/td><�td> 6.54 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Ti <�/td><�td> 22 <�/td><�td> 43.266 <�/td><�td> 27.491 <�/td><�td> 13.58 <�/td><�td> 6.82 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> V <�/td><�td> 23 <�/td><�td> 65.23 <�/td><�td> 46.707 <�/td><�td> 29.31 <�/td><�td> 14.65 <�/td><�td> 6.74 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Cr <�/td><�td> 24 <�/td><�td> 90.56 <�/td><�td> 69.3 <�/td><�td> 49.1 <�/td><�td> 30.96 <�/td><�td> 16.5 <�/td><�td> 6.766 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Mn <�/td><�td> 25 <�/td><�td> 119.27 <�/td><�td> 95 <�/td><�td> 72.4 <�/td><�td> 51.2 <�/td><�td> 33.667 <�/td><�td> 15.64 <�/td><�td> 7.435 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Fe <�/td><�td> 26 <�/td><�td> 151.06 <�/td><�td> 125 <�/td><�td> 99 <�/td><�td> 75 <�/td><�td> 54.8 <�/td><�td> 30.651 <�/td><�td> 16.18 <�/td><�td> 7.87 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Co <�/td><�td> 27 <�/td><�td> 186.13 <�/td><�td> 157 <�/td><�td> 129 <�/td><�td> 102 <�/td><�td> 79.5 <�/td><�td> 51.3 <�/td><�td> 33.5 <�/td><�td> 17.06 <�/td><�td> 7.86 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Ni <�/td><�td> 28 <�/td><�td> 224.5 <�/td><�td> 193 <�/td><�td> 162 <�/td><�td> 133 <�/td><�td> 108 <�/td><�td> 75.5 <�/td><�td> 54.9 <�/td><�td> 35.17 <�/td><�td> 18.168 <�/td><�td> 7.635 <�/td><�td> <�/td><�td> <�/td><�/tr>
<�tr><�td> Cu <�/td><�td> 29 <�/td><�td> 266 <�/td><�td> 232 <�/td><�td> 199 <�/td><�td> 166 <�/td><�td> 139 <�/td><�td> 103 <�/td><�td> 79.9 <�/td><�td> 55.2 <�/td><�td> 36.83 <�/td><�td> 20.292 <�/td><�td> 7.726 <�/td><�td> <�/td><�/tr>
<�tr><�td> Zn <�/td><�td> 30 <�/td><�td> 310.8 <�/td><�td> 274 <�/td><�td> 238 <�/td><�td> 203 <�/td><�td> 174 <�/td><�td> 134 <�/td><�td> 108 <�/td><�td> 82.6 <�/td><�td> 59.4 <�/td><�td> 39.722 <�/td><�td> 17.964 <�/td><�td> 9.394 <�/td><�/tr>
<�tr><�td> Ga <�/td><�td> 31 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 64 <�/td><�td> 30.71 <�/td><�td> 20.51 <�/td><�/tr>
<�tr><�td> Ge <�/td><�td> 32 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 93.5 <�/td><�td> 45.71 <�/td><�td> 34.22 <�/td><�/tr>
<�tr><�td> As <�/td><�td> 33 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 127.6 <�/td><�td> 62.63 <�/td><�td> 50.13 <�/td><�/tr>
<�tr><�td> Se <�/td><�td> 34 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 155.4 <�/td><�td> 81.7 <�/td><�td> 68.3 <�/td><�/tr>
<�tr><�td> Br <�/td><�td> 35 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 192.8 <�/td><�td> 103 <�/td><�td> 88.6 <�/td><�/tr>
<�tr><�td> Kr <�/td><�td> 36 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 230.39 <�/td><�td> 126 <�/td><�td> 111 <�/td><�/tr>
<�tr><�td> Rb <�/td><�td> 37 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 277.1 <�/td><�td> 150 <�/td><�td> 136 <�/td><�/tr>
<�tr><�td> Sr <�/td><�td> 38 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 324.1 <�/td><�td> 177 <�/td><�td> 162 <�/td><�/tr>
<�tr><�td> Y <�/td><�td> 39 <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> <�/td><�td> 374 <�/td><�td> 206 <�/td><�td> 191 <�/td><�/tr>
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