Important Trends in the Periodic Table

The properties of the elements exhibit trends. These properties can be predicted using the periodic table and can be explained and understood by analyzing the electron configurations of the elements. Elements tend to gain or lose valence electrons to achieve stable octet formation. Stable octets are seen in the inert gases, or noble gases, of Group 18 of the periodic table.

 

Shielding

Electrons on the outside energy level (valence electrons) have the inner energy levels (kernel electrons) blocking the nucleus positive force field. These inside energy level electrons shield (block) the nuclear force field from the valence electrons. As you go across a row (period) the number of inside electrons is constant. The number of inside energy levels stays the same and these core levels are full. As you go across the row the nuclear charge gets larger (the force field gets bigger) because a proton is added to the nucleus. As you go across the row there a valence electron is added to the valence shell but the valence electrons have the same shielding.

An analogy would be a lamp with a shade. What would happen to the amount of light getting out to the room if we used: a 25 watt bulb, then a 40 watt bulb, then a 60 watt bulb and finally a 100 watt bulb? The amount of light passing through the shielding shade increases with the increasing strength of the light.

 

 

 

 

 

 

 

As we go across the period there are protons added to the nucleus; the positive force field is getting stronger (more protons in the nucleus). The kernel (number of shielding electrons) stays the same; so there is more positive force field getting out to the valence electrons. The stronger positive force field attracts the electrons more strongly.

Notice the size of the nuclear charge (positive force field) increase from +3 to +10 across the row. The number of inner (core) electrons remains the same (2e) across the row. The inner 2e are between the nucleus and the valence electrons. The blocking strength (shielding effect) of these inner electrons is the same across the row. Across the row the valence electrons will have a greater attraction to the nucleus because of the greater nuclear charge. The shielding becomes less effective across the row 2e can shield +3 better than 2e can shield +10. The valence electrons in Ne feel a greater positive force field and are more strongly attracted to the nucleus. The valence electron in Li is effectively shielded from the positive force field of the nucleus and is very weakly attracted to the nucleus (metals are born losers lose valence electrons easily).

 

What happens to the attraction to valence electrons as you go down a column (family or group)? As you move from one period to the next the valence electrons are being added to a new valence shell (energy level) that is further from the nucleus. As valence shells are filled additional valence electrons must be placed in larger energy levels that are further from the nucleus. These new valence electrons have additional levels of inner shielding electrons (are more effectively shielded from the nuclear charge). As you go down the group, the attraction of the valence electrons to the nucleus decreases because the valence electrons are further from the nucleus and are better shielded from the nuclear force field.

 

These shielding effects lead to some very important Periodic Trends observed in the elemental properties of atomic radius, ionization energy, electron affinity, and electronegativity.

 

Atomic Radius

Atomic Radius equals half the distance between two nuclei of a diatomic molecule.

Table of atomic radii in nonometres (10-9m)

H 0.030

 

/

 

 

 

 

 

Li 0.123

Be 0.089

\

B 0.080

C 0.077

N 0.070

O 0.066

F 0.064

Na 0.157

Mg 0.136

/

Al 0.125

Si 0.117

P 0.110

S 0.104

Cl 0.099

K 0.203

Ca 0.174

\

Ga 0.125

Ge 0.122

As 0.121

Se 0.117

Br 0.114

Rb 0.216

Sr 0.191

/

In 0.150

Sn 0.140

Sb 0.140

Te 0.137

I 0.133

 

 

\

 

 

 

 

 

 

PART I

Questions:

1.      Use the attached graph to plot Atomic Radius vs Atomic number for periods 2 to 5 for the representative elements given above.

2.      What does the graph and data table show for trends in Atomic Radius as you move across a period and as you move down a group?

 

Looking at the table of values for atomic radius and your graphs you may note:

Period trends

As you go across a period the radius gets smaller. The smallest atoms in each period (row) will be to the right; the size decreases as you move right along the row. Within a Period the charge on nucleus increases the larger charge pulls valence electrons which are all in the same shell in closer. How do we explain this in terms of the shielding of the valence electrons and the effective nuclear charge?

Group trends

As we go down a group, the number of filled energy shells increases, each atom has an additional energy level. The higher energy level is further away from the nucleus so the atoms get bigger, valence electrons have very weak attraction to the nucleus. The largest atoms are found at the bottom of each group. The size of the atom increases as you move down the family.

 

Ionization Energy

Much of our knowledge of matter has been obtained by using the tactic of "jolting" atoms with energy and examining the effects. The energy can be in the form of electromagnetic radiation (light, microwaves, X-rays etc.) or the kinetic energy of moving particles (such as electrons and alpha particles). We have already seen how Rutherford bombarded thin sheets of metal foils with alpha particles and interpreted from his observations that almost all the mass of the atom is concentrated in a lump in the center called the nucleus. Most of the volume of the atom was interpreted to be due to the electron cloud. We have also seen how Neils Bohr, a student of Rutherford, studied the light emitted by gases when they were struck by fast electrons. He concluded that the electrons in atoms can have only certain energy values (energy levels) and not others.

The ionization energy, or ionization potential, is the energy required to completely remove an electron from a gaseous atom or ion. The closer and more tightly bound an electron is to the nucleus, the more difficult it will be to remove, and the higher its ionization energy will be.

The first ionization energy is the energy required to remove one electron from the parent atom. The second ionization energy is the energy required to remove a second valence electron from the univalent ion to form the divalent ion, and so on.

One way we can model the electron cloud is to interpret ionization energy data. Scientists have measured the amount of energy required to knock an electron completely away from the atom. This process forms ions and hence the energy is called the ionization energy. Below is a simplified diagram of an apparatus used to measure ionization energies.

 

 

A sample of say, sodium, is vapourized and admitted to the vacuum chamber. With the filament glowing and the power source adjusted to give a small voltage difference between filament and plate, a stream of electrons flows across the chamber from the left to right. Some of these will collide with sodium vapour atoms. If the power supply is set for less than five volts, no damage is done; the electrons rebound and continue their journey to the plate. At just above 5.1 volts, however, there is a dramatic increase in the current flowing through the ammeter. An electron with 5.2 volts of energy is moving fast enough to knock an electron away from an isolated sodium vapour atom. This suddenly increases the population of free charged particles in the vacuum chamber, giving an increase in current.

 

Na(g) + energy Na+(g) + e-

 

Having knocked an electron from sodium at 5.2 volts can we do further damage at higher voltages? We can! At just over 47 volts, another flood of electrons increasing the current reveals that a second ionization has taken place:

 

Na+(g) + energy Na2+(g) + e-

 

A powerful instrument can continue until the atom is stripped bare of its electrons. From the voltage used to accelerate the electrons, the ionization energy can be calculated.

 

These successive ionization energies always increase in value. The charge in the nucleus stays the same but as we remove electrons the repulsions in the cloud decrease. This results in a relatively stronger attraction to the nucleus and a corresponding larger energy required to remove succeeding electrons.

 


Successive Ionization Energy Values (kJ/mol)

Ionization

Number

 

H

He

Li

Be

B

C

N

O

F

Ne

Na

Mg

Al

Si

P

S

Cl

Ar

1

1312

2371

520

900

800

1086

1402

1314

1681

2080

496

738

578

786

1012

1000

1251

1520

2

 

5248

7244

1738

2455

2344

2884

3388

3388

3981

4571

1451

1817

1577

1903

2251

2297

2666

3

 

 

11749

14791

3631

2291

4571

5248

6026

6166

6918

7733

2745

3232

2912

3361

3822

3931

4

 

 

 

20893

25119

6166

7413

7413

8318

9333

6310

10540

11577

4356

4957

4564

5158

5771

5

 

 

 

 

33113

38019

9550

10965

10965

12302

13490

 

 

16091

6274

7013

6542

7238

6

 

 

 

 

 

46774

53703

13183

15136

15136

16596

 

 

19785

21269

8496

9362

8781

7

 

 

 

 

 

 

64565

70795

17783

19953

19953

 

 

 

 

27106

11018

11955

8

 

 

 

 

 

 

 

83176

91201

22909

25704

 

 

 

 

31670

33604

13842

9

 

 

 

 

 

 

 

 

107152

114815

28840

 

 

 

 

 

38600

40760

10

 

 

 

 

 

 

 

 

 

131826

141254

 

 

 

 

 

43961

46186

11

 

 

 

 

 

 

 

 

 

 

169824

 

 

 

 

 

 

 

 

The following series of questions and the information above will show another way of gaining information about the structure of the electron cloud of the atom.

 

PART II

Questions:

1.      Use the attached graph paper to plot the 1st ionization energy vs Atomic number.

2.      What does the graph and data table show for trends in ionization energies as you move across a period and as you move down a group?

3.      What does this graph show about full energy level; full sublevels and full sublevels?

 

PART III

Questions

1.      For sodium plot the ionization energy vs ionization number (IE1 through IE11).

2.      Does this data suggest that the attraction of the nucleus for the first electron was greater or smaller than that felt for the second electron removed?

3.      What does this large increase (nine fold) suggest about the relative distance from the nucleus of the first electron removed compared to the second one removed?

4.      Following this nine fold increase, the ionization energies go up by smaller amounts for the next 8 electrons (see the graph). What conclusion can be made about these 8 electrons in terms of their probable distance from the nucleus?

5.      Further examination of the ionization data and the graph, reveals another large jump in the ionization energy between IE9 and IE10. What might be interpreted about the tenth electron and its relative distance from the nucleus? Explain your conclusion.

6.      How does this graph show the existence of energy levels?

7.      The electrons which occur in the outermost energy level are the most likely ones to interact with other atoms in chemical changes. These electrons are called VALENCE ELECTRONS. How many valence electrons do sodium atoms have?

 

 

 

 

CONCLUSION:

These successive ionization energies reveal a hidden "staircase" of energy levels within the atom. The large jumps between IE1 and IE2 and IE9 and IE10 suggest where the levels change from one level to another level.


We might picture an energy level diagram for sodium at this point as follows:

 

Energy Number of Electrons in the level

Level

3 ------------- (1) (least strongly attracted)

 

2 ------------- (8)

 

1 ------------- (2) (attracted most strongly)

 

ENERGY LEVEL DIAGRAM FOR SODIUM

 

It is now time to write a report on what you have learned about Periodic Trends so far. Your report should include: Purpose; Procedure; Processing the data (analysis of the data); conclusion and answers to the questions. HAND IN YOUR REPORT ON PARTS I, II and III

 

PART IV

Use the table of successive ionization energies for elements 1 to 18 on the page above to answer the following.

Questions

1.      Indicate where the major jumps in ionization energy occur.

2.      Make an interpretation concerning the number of electrons in the lowest energy level.

3.      Make an interpretation concerning the number of valence electrons.

4.      Which elements have the same number of valence electrons?

5.      In phosphorus atoms

(a)    Explain why there is such a large jump between IE3 and IE4.

(b)   Explain why there is such a large jump between IE5 and IE6.

6.      What relationship exists between the number of valence electrons and the position of the element on the periodic table?

 

 

CONCLUSION:

What determines Ionization Energy?

1. As the distance from the nucleus increases the attraction to the nucleus decreases. As the attraction to the nucleus decreases the ionization energy decreases. It is easier to remove an electron that is farther from the nucleus.

2. The greater the effective nuclear charge (smaller shielding of valence electrons) the greater the force of attraction to the valence electrons. The stronger the attraction for valence electrons the more energy is needed to remove a valence electron.

3. Filled and half filled sublevels have lower energy, so these configurations would have higher ionization energies, harder to remove an electron from lower energy.

 

Period trends

All the atoms in the same period have the same valence energy level and the same shielding. The increasing nuclear charge increases the attraction of valence electrons so ionization energy generally increases from left to right. The exceptions at full and filled sublevels break the pattern because removing an electron from a stable (low energy) configuration will require more energy. Li has a low 1st ionization because 2 core electrons block the +3 nuclear charge more than they could block the +10 nuclear charge in the Ne atom that would have large ionization energy.

 

Group trends

As you go down a group, first ionization energy decreases because the valence electron is further away and there are more inner electrons causing more shielding. Ne has lower ionization energy than He even though both are full energy levels because Ne has more shielding and valence electrons are a greater distance from the nucleus.

 

Driving Force why atoms react

Atoms with a full outer energy level (valence shell) are very low in energy. Noble gases have full valence shells and are therefore very stable elements (not reactive). The Noble gases are like trendsetters while the other elements are wannabes. Atoms behave in ways to achieve the stable noble gas configuration.

 

Electron Affinity

Electron Affinity is the energy change associated with adding an electron to a gaseous atom. If the atom becomes more stable (electron configuration like the noble gases) there is a loss of energy and the energy change is shown a negative value.

F(g) + e- → F-(g) + 328 kJ (EA = -328kJ)

If the atom becomes less stable the energy level goes up and the energy change is shown as a positive value.

Be(g) + e- + 240kJ → Be-(g) (EA = +240kJ)

The ability to attract an extra electron depends on the strength of attraction of valence electrons. Strong attraction of valence electrons means a greater the ability to hold an extra electron.

Electron Affinity for the Representative Elements (EA) (kJ/mole)

H -73

 

/

 

 

 

 

 

Li -60

Be +240

\

B -27

C -122

N +9

O -141

F -328

Na -53

Mg +230

/

Al -44

Si -134

P -72

S -200

Cl -348

K -48

Ca +156

\

Ga -30

Ge -120

As -77

Se -195

Br -325

Rb -47

Sr +170

/

In -30

Sn -121

Sb -101

Te -190

I -295

Cs -45

Ba +52

\

Tl -30

Pb -110

Bi -110

Po -183

At -270

 

PART V

Questions

  1. What does the data table show for trends in electron affinity values as you move across a period and as you move down a group?
  2. Explain these trends:

a)      in values in terms of the shielding of valence electrons

b)      the stability of sublevels or energy levels.

 

 

Period trends

Electron affinity is low for metals and high for nonmetals. It is easiest for group 7Ato get and hold an extra electron because it gets them to full energy level. Electron affinity increases from left to right as atoms become smaller, with greater nuclear charge and get closer to a full energy level.

 

Group trends

Electron affinity decreases as we go down a group because the atoms are getting bigger and the valence electrons are not attracted as strongly to the nucleus.

 

Ionic Size

Cations form atoms by losing electrons. Cations are smaller that the atom they come from. There are fewer electrons with the same nuclear charge, leading to a greater attraction of the remaining electrons smaller particle. Metals form cations. Cations of representative elements have noble gas configuration.

Anions form by atoms gaining electrons. Anions are bigger that the atom they come from because there are more electrons being held by the same nuclear charge. Nonmetals form anions. Anions of representative elements have noble gas configuration.

 

Table of Ionic Radii in nonometres (10-9m)

Li+ 0.060

Be2+ 0.031

\

B3+ 0.020

C4+ 0.015

N3- 0.171

O2- 0.140

F- 0.136

Na+ 0.095

Mg2+ 0.065

/

Al3+ 0.050

Si4+ 0.041

P3- 0.212

S2- 0.184

Cl- 0.181

K+ 0.133

Ca2+ 0.099

\

Ga3+ 0.062

Ge4+ 0.053

As3- 0.222

Se2- 0.198

Br- 0.195

Rb+ 0.148

Sr2+ 0.113

/

In3+ 0.081

Sn4+ 0.071

Sb3- 0.245

Te2- 0.221

I- 0.216+

Cs+ 0.169

Ba2+ 0.135

\

Tl3+ 0.095

Pb4+ 0.084

 

 

 

 

Configuration of Ions

Representative ions always have noble gas configuration. Na is 1s12s22p63s1 . Sodium forms a +1 ion - 1s12s22p6 that is the same configuration as neon. Metals form ions with the configuration of the noble gas before them - they lose electrons.

Non-metals form ions by gaining electrons to achieve noble gas configuration. They end up with the configuration of the noble gas after them.

 

 

 

 

 

Group trends

Ions get bigger as you go down because the ion has added energy levels.

Period Trends

Across the period nuclear charge increases and energy level changes when the positive ions form. Cations revert back to the previous energy level by losing electrons to attain the previous noble gas configuration., The cations get smaller as you move right because the cations lose one more electron as you move right. Sodium loses the s1 electron, Mg loses the two s2 electrons and the Al loses the three s2p1 electrons. Each cation is isoelectronic (ions have the same number of electrons) with Ne (same electronic configuration). Na1+ has +11 attracting 10e; Mg2+ has +12 attracting 10e and Al3+ has +13 attracting 10e. The ionic size of cations decreases as you move right

Anions gain electrons to form the stable electron configuration. Nitrogen gains 3e(N-3), Oxygen gains 2e (O-2) and Fluorine gains 1e(F-1). Each of the anions will look like Ne(all have 10 electrons). N has +7 attracting 10e, O has +8 attracting 10e and F has +9 attracting 10e. N attraction will be weakest and F attraction will be strongest. The size of the anion decreases as you move right. The anions are bigger than the cations because of the extra energy level in the anion.

 

Electronegativity

Electronegativity is a measure of the attraction of an atom for the electrons in a chemical bond. The higher the electronegativity of an atom, the greater its attraction for bonding electrons. Electronegativity is related to ionization energy. Electrons with low ionization energies have low electronegativities because their nuclei do not exert a strong attractive force on electrons. Elements with high ionization energies have high electronegativities due to the strong pull exerted on electrons by the nucleus. Atoms that have strong attraction to their own valence electrons will be able to attract the valence electrons from other atoms. (Atoms with large negative electron affinity have larger electronegativity.)

Electronegativity values are expressed in arbitrary units on the Pauling electronegativity scale (based on electron affinity and ionization potential of the atoms).

2.1
H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0
Li

1.5
Be

 

 

 

 

 

 

 

 

 

 

2.0
B

2.5
C

3.0
N

3.5
O

4.0
F

1.0
Na

1.2
Mg

 

 

 

 

 

 

 

 

 

 

1.5
Al

1.8
Si

2.1
P

2.5
S

3.0
Cl

0.9
K

1.0
Ca

1.3
Sc

1.4
Ti

1.5
V

1.6
Cr

1.6
Mn

1.7
Fe

1.7
Co

1.8
Ni

1.8
Cu

1.6
Zn

1.7
Ga

1.9
Ge

2.1
As

2.4
Se

2.8
Br

0.9
Rb

1.0
Sr

1.2
Y

1.3
Zr

1.5
Nb

1.6
Mo

1.7
Tc

1.8
Ru

1.8
Rh

1.8
Pd

1.6
Ag

1.6
Cd

1.6
In

1.8
Sn

1.9
Sb

2.1
Te

2.5
I

0.8
Cs

1.0
Ba

1.1
La

1.3
Hf

1.4
Ta

1.5
W

1.7
Re

1.9
Os

1.9
Ir

1.8
Pt

1.9
Au

1.7
Hg

1.6
Tl

1.7
Pb

1.8
Bi

1.9
Po

2.1
At

 

Part VI - Question

  1. What does the data table show for trends in electronegativity values as you move across a period and as you move down a group?
  2. Explain these trends in values in terms of the shielding of valence electrons and the completion of energy levels.

 

Period Trend

Metals are at the left have weak attraction for valence electron due to the shielding effect. Metals let their electrons go easily (born losers). Metals have low electronegativity. At the right end are the nonmetals that have strong attraction to valence electrons due to poor shielding. Nonmetals have valence shells that are almost full so they want more electrons and are able to hold them. Nonmetals have high electronegativity. Electronegativity increases as you move across the period.

Group Trend

The further down a group the farther the valence electrons are away from the nucleus and the more inner electrons an atom has to shield the valence electrons. The valence electrons are not held as tightly. As you move down the group the attraction to the valence electrons decreases so the electronegativity will decrease as you move down the group.

 

HAND IN YOUR REPORT ON PARTS IV, V and VI

 

 

A summary of Periodic Trends

 

Atomic size decreases

Ionization energy increases

Electron affinity increases

Electronegativity increases

Nuclear charge increases

Shielding effect decreases

 

 

 

 

 

 

 

 


1

 

 

 

 

 

 

 

 

18

 

2

 

 

13

14

15

16

17

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Text Box: Atomic radius (size) increases
Ionization energy decreases
Electron affinity decreases
Electronegativity decreases

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Atomic Radius vs Atomic number

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Text Box: Radii (nonometers)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Atomic number


1st ionization energy vs Atomic number

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Successive ionization energies of Sodium