Atomic and Ionic Sizes. (2023)

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7.2Atomic and Ionic Sizes

learning goals

  1. Understand periodic trends in atomic radii.
  2. Predicting relative sizes of ions within an isoelectronic series.

Although some people fall into the trap of visualizing atoms and ions as small, hard spheres similar to miniature ping-pong balls or miniature marbles, the quantum mechanical model tells us that their shapes and boundaries are much less defined than these images. suggest. Therefore, atoms and ions cannot be said to have exact sizes. In this section, we discuss how atomic and ionic "sizes" are defined and conserved.

the atomic radius

to rememberChapter 6 "The Structure of Atoms"that the probability of finding an electron in the various available orbitals slowly decreases with increasing distance from the nucleus. This point is illustrated inFigure 7.4 "Plots of radial probability versus distance from the nucleus for He, Ne and Ar", showing a plot of the total electron density for all occupied orbitals of three noble gases as a function of their distance from the nucleus. Electron density gradually decreases with increasing distance, making it impossible to draw a sharp line marking the boundary of an atom.

Figure 7.4Radial Probability versus Core Distance Plots for He, Ne, and Ar

Atomic and Ionic Sizes. (3)

In it is the 1SElectrons have a maximum radial probability at ≈30 pm from the nucleus. In Ne, the 1stSelectrons have a maximum at ≈8 pm, and the 2Se 2Pageelectrons combine to another maximum at ≈35 pm (thenorte= 2 bark). In Air, the 1stSElectrons have a maximum at ≈2 pm, the 2Se 2Pageelectrons combine at most at ≈18 pm, and the 3Se 3Pageelectrons combine to a maximum at ≈70 pm.

(Video) Ionic and Atomic Radius - Periodic Trends

Figure 7.4 "Plots of radial probability versus distance from the nucleus for He, Ne and Ar"it also shows that there are clear peaks in total electron density at certain distances and that these peaks occur at different distances from the nucleus for each element. Each peak on a given plot corresponds to the density of electrons in a given main shell. Since helium has only one filled shell (norte=1), shows a single peak. Contrast, neon, fullnorte=1 and 2 main layers, has two peaks. filled with argonnorte=1, 2 and 3 main shells, has three points. The summit for allnorte= 1 projectile occurs at increasingly shorter distances for neon (Z=10) and argon (Z=18) because their nuclei are more positively charged than helium with a higher number of protons. why the 1S2layer is closer to the nucleus, its electrons are very poorly shielded by electrons in filled layers with higher valuesnorte. Consequently, the two electrons in thenorte= 1 shell experiences almost all of the nuclear charge, resulting in a strong electrostatic interaction between the electrons and the nucleus. the energy ofnorte= 1 bowl also decreases significantly (the 1 fullSorbital becomes more stable) as the nuclear charge increases. For similar reasons, fillingnorte=2 shell, in which the argon is closer to the nucleus and has energy less than thenorte=2 bowl in neon.

Figure 7.4 "Plots of radial probability versus distance from the nucleus for He, Ne and Ar"illustrates the difficulty of measuring the dimensions of a single atom. However, because the distances between nuclei in pairs of covalently bonded atoms can be measured quite accurately, chemists use these distances as a basis for describing approximate atomic sizes. For example, the internuclear distance in diatomic Cl2the molecule is known to be 198 pm. We assign half this distance to each chlorine atom and give chlorine akovalenter Atomradius (Rto be)Half the distance between the nuclei of two identical atoms joined by a covalent bond in the same 99 pm o 0.99 Å (parte (a) enFigure 7.5 “Atomic radius definitions”).Atomic radii are usually measured in angstroms (Å), a non-SI unit: 1 Å = 1 × 10−10m = 100 hours.

Figure 7.5Definition of Atomic Radius

Atomic and Ionic Sizes. (4)

(a) Der covalent Atomradius,Rto be, is half the distance between the nuclei of two identical atoms joined by a covalent bond in the same molecule, such as B.Cl2. (b) The metallic atomic radius,Rmeet, is half the distance between the nuclei of two adjacent atoms in a pure solid metal like aluminum. (c) The van der Waals atomic radius,RvdW, is half the distance between the nuclei of two identical atoms, such as argon, that are close to each other but not bonded. (d) This is a plot of covalent chlorine versus van der Waals radii.

In a similar approach, we can use the lengths of carbon-carbon single bonds in organic compounds, which are remarkably uniform at 154 pm, to assign a value of 77 pm as the covalent atomic radius of carbon. If these values ​​really reflect the actual sizes of atoms, we should be able to predict the lengths of covalent bonds between different elements by adding them together. For example, for a C-Cl bond, we could predict a carbon-chlorine distance of 77 pm + 99 pm = 176 pm, which is very close to the average value observed for many organochlorine compounds.A similar approach to measuring ion size is discussed later in this section.

Covalent atomic radii can be determined for most nonmetals, but how do chemists obtain atomic radii for elements that do not form covalent bonds? A variety of other processes have been developed for these elements. With a metal, for example thatmetallic atomic radius (Rmeet)Half the distance between the nuclei of two adjacent metal defined as half the distance between the nuclei of two adjacent metal atoms (part (b) inFigure 7.5 “Atomic radius definitions”). For elements such as the noble gases, many of which do not form stable compounds, we can use so-calledVan der Waals Atom RadiusRvdW)Half the internuclear distance between two unbonded atoms in a solid., which is half the internuclear distance between two unbonded atoms in the solid (part (c) inFigure 7.5 “Atomic radius definitions”). An atom like chlorine has a covalent radius (the distance between the two atoms in a Cl2molecule) and a van der Waals radius (the distance between two Cl atoms in different molecules, e.g. Cl2(s) at low temperatures). These radii are usually not equal (part (d) inFigure 7.5 “Atomic radius definitions”).

Periodic trends in atomic radii

Since it is impossible to measure the size of metallic and non-metallic elements using a single method, chemists have developed a consistent way to calculate atomic radii using the quantum mechanical functions described inChapter 6 "The Structure of Atoms". Although the radii values ​​obtained by such calculations are not identical to any of the experimentally measured values, they do provide a way to compare the intrinsic sizes of all elements and clearly show that atomic size varies periodically (Figure 7.6 "Graph of the periodic variation of the atomic radius with atomic number for the first six rows of the periodic table"). On the periodic table, atomic radii decrease in a row from left to right and increase in a column from top to bottom. Because of these two trends, the largest atoms are in the lower left corner of the periodic table and the smaller ones in the upper right corner (Figure 7.7 "Calculated atomic radii (in picometers) of the ").

Figure 7.6A graph of the periodic change in atomic radius with atomic number for the first six rows of the periodic table

Atomic and Ionic Sizes. (5)

It is similar to the plot of atomic volume versus atomic number (Figure 7.2 "Variation of atomic volume with atomic number, adapted from the 1870 Meyer diagram") – a variation of Meyer's opening plot.

Figure 7.7Calculated atomic radii (in picometers) ofS-,Page-,jD-Block items

Atomic and Ionic Sizes. (6)

The sizes of the circles illustrate the relative sizes of atoms. The calculated values ​​are based on quantum mechanical wave functions.

note the pattern

Atomic radii decrease from left to right in a row and increase from top to bottom in a column.

Trends in atomic size result from differences ineffective atomic charge (ZIt is made)experienced by electrons in the outermost orbitals of elements. As we described inChapter 6 "The Structure of Atoms", for all elements except H, the effective nuclear charge is alwaysnot lessthan the actual nuclear charge due to shielding effects. The greater the effective nuclear charge, the more the outermost electrons are attracted to the nucleus and the smaller the atomic radius becomes.

The atoms in the second row of the periodic table (Li to Ne) illustrate the effect of electronic shielding. (For more information on electron shielding, seeChapter 6 "The Structure of Atoms",Section 6.5 “Atomic Orbitals and Their Energies”, jFigure 6.29 "Orbital energy level diagram for a typical multi-electron atom".) All have 1 completedS2inner layer, but if we go from left to right along the line, the nuclear charge increases from +3 to +10. Although electrons are added to the 2ndSe 2PageOrbital,Electrons in the same main shell are not very effective at shielding each other from nuclear charge.. Also Die Single 2SThe electron in lithium experiences an effective nuclear charge of about +1 because the electrons in the filled 1S2Shell effectively neutralizes two of the three positive charges in the core. (More detailed calculations give a value ofZIt is made=+1.26 for Li.) Conversely, the two 2SThe electrons in beryllium don't shield each other very well, even though the 1 is filled.S2Shell effectively neutralizes two of the four positive charges in the core. This means that the effective nuclear charge of the 2ndSThe electrons in beryllium range from +1 to +2 (the calculated value is +1.66). Consequently, beryllium is significantly smaller than lithium. Likewise, as we go down the series, the increasing nuclear charge is not effectively neutralized by the electrons added to 2Se 2PageOrbitals The result is a constant increase in effective nuclear charge and a constant decrease in atomic size.

Atomic and Ionic Sizes. (7)

The increase in atomic size along a column is also due to the shielding of electrons, but the situation is more complex because of the principal quantum numbernorteis not constant, as we have seenChapter 6 "The Structure of Atoms", the size of the orbitals increasesnorteincreases,as long as the nuclear charge remains the same. For example, in Group 1, the size of atoms increases significantly along the column. At first it may seem reasonable to attribute this effect to the successive addition of electronsnsOrbitals with increasing values ​​ofnorte. However, it is important to remember that the radius of an orbital is highly dependent on the nuclear charge. If we move down the column of group 1 elements, the principal quantum numbernorteincreases from 2 to 6, but core charge increases from +3 to +55! If cesium's outermost electrons experienced the full nuclear charge of +55, a cesium atom would be very small indeed. In fact, the effective nuclear charge perceived by the outermost electrons in cesium is much smaller than expected (6 instead of 55). This means that cesium with a 6S1valence electron configuration, is much larger than lithium, with 2S1valence electron configuration. The effective nuclear charge changes relatively little from lithium to cesiumThe electrons in the filled inner shells are very effective in shielding the outer shell electrons from the nuclear charge.. Although cesium has a nuclear charge of +55, it has 54 electrons in its 1 filled.S22S22Page63S23Page64S23D104Page65S24D105Page6shells, abbreviated as [Xe]5S24D105Page6, which effectively neutralize most of the 55 positive charges in the nucleus. The same dynamic is responsible for the constant increase in magnitude observed as we move through the other columns of the periodic table. The irregularities can usually be explained by fluctuations in the effective nuclear charge.

(Video) Practice Problem: Atomic Radii and Ionic Radii

note the pattern

Electrons in the same main shell are not very effective at shielding each other from nuclear charge, while electrons in filled inner shells are very effective at shielding electrons in outer shells from nuclear charge.

example 2

Arrange these elements in order of increasing atomic radii based on their positions on the periodic table: aluminum, carbon, and silicon.

Given:three elements

At the request of:Arrange in order of increasing atomic radius


AIdentify the position of elements in the periodic table. Determining the relative size of elements that are in the same column as their principal quantum numbernorte. Then determine the order of the elements in the same row from their effective nuclear charges. If items are not in the same column or row, use paired comparisons.

BSort the elements in order of increasing atomic radius.


AThese items are not all in the same column or row, so we need to use paired comparisons. Carbon and silicon are in group 14 with carbon at the top, so carbon is smaller than silicon (C<Si). Aluminum and silicon are in the third row with aluminum on the left, so silicon is smaller than aluminum (Si<Al) because its effective nuclear charge is greater.BCombining the two inequalities gives the general order: C<Si<Al.

a practice

Arrange these elements in order of increasing magnitude based on their positions on the periodic table: oxygen, phosphorus, potassium, and sulfur.


Ionic Radii and Isoelectronic Series

How did you learnChapter 2 "Molecules, Ions, and Chemical Formulas"ionic compounds consist of regularly repeating sets of alternating cations and anions. Although it is not possible to directly measure an ionic radius from which it is not possible to directly measure the radius of an atom, for the same reason it isesIt is possible to measure the distance between the nuclei of a cation and a neighboring anion in an ionic compound to determine the distanceIonenradiusThe radius of a cation or anion.of one or both. as shown inFigure 7.8 "Definition of the ionic radius", the distance from the nucleus corresponds to thatadditivethe cation and anion radii. A variety of methods have been developed to proportionally divide the experimentally measured distance between the smallest cation and the largest anion. These methods produce sets of ionic radii that are internally consistent from one ionic compound to another, although each method produces slightly different values. For example, the radius of Na+The ion is essentially the same in NaCl and Na2Yes, as long as the same measurement method is used. Despite small methodological differences, certain trends can be observed.

Figure 7.8Definition of ionic radius

Atomic and Ionic Sizes. (8)

(a) The internuclear distance is distributed between neighboring cations and anions in the ion structure, as shown here for Na+y Klin sodium chloride. (b) This contour plot of electron density for a single atomic plane in the NaCl structure shows how lines connect points of equal electron density. Note the relative magnitudes of the electron density contour lines around Clme in+.

A comparison of ionic radii with atomic radii (Figure 7.9 "Ionic radii (in picometers) of the most common oxidation states of") shows that athe cation is always smaller than its neutral parent atom, and an anion is always larger than its neutral parent atom. When one or more electrons are removed from a neutral atom, two things happen: (1) the repulsions between electrons in the same main shell decrease because there are fewer electrons, and (2) the effective nuclear charge seen by the remaining electrons increases. because there are fewer electrons protecting each other from the nucleus. Consequently, the size of the region of space occupied by electrons decreases (compare Li at 167 pm with Li+after 76 hours). If different numbers of electrons can be removed to produce ions with different charges, the ion with the largest positive charge is the smallest (compare Fe2+at 78 with faith3+at 64.5 hours). On the other hand, adding one or more electrons to a neutral atom causes the electron-electron repulsion to increase and the effective nuclear charge to decrease, increasing the size of the probability region (compare F at 42 pm with Fat 1:33 p.m.).

Figure 7.9Ionic radii (in picometers) of the most common oxidation states ofS-,Page-,jD-Block items

Atomic and Ionic Sizes. (9)

Gray circles indicate ion sizes shown; the colored circles indicate the size of the neutral atoms shown earlier inFigure 7.7 "Calculated atomic radii (in picometers) of the ".

Quelle: Daten zu Ionenradien von R. D. Shannon, „Revised Effective ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides“.crystallographic record32, nº. 5 (1976): 751-767.

(Video) The Periodic Table: Atomic Radius, Ionization Energy, and Electronegativity

note the pattern

Cations are always smaller than the neutral atom and anions are always larger.

Since most elements form either a cation or an anion, but not both, there is little opportunity to compare the sizes of a cation and anion that come from the same neutral atom. However, some sodium compounds contain Naion, allowing its size to be compared to that of the much better known Na+ion found inmanyConnections. The radius of sodium in each of its three known oxidation states is given inTable 7.2 "Experimentally measured values ​​for the radius of sodium in its three known oxidation states". All three types have a nuclear charge of +11, but contain 10 (Na+), 11 (Na0), y 12 (Na) electrons. then a+ion is significantly smaller than the neutral Na atom because the thirdS1one electron has been removed to give a closed shell withnorte=2. then aion is larger than the Na atom because the extra electron creates a 3S2valence electron configuration while the nuclear charge remains the same.

Table 7.2Experimentally measured values ​​for the radius of sodium in its three known oxidation states

Von+ Von0 Von
electronic configuration 1S22S22Page6 1S22S22Page63S1 1S22S22Page63S2
Radio (afternoon) 102 154* 202
*Radium metal measured for Na(s).
Fonte: M. J. Wagner e J. L. Dye, „Alkalides, Electrides, and Expanded Metals“,Materials Science Annual Review23 (1993): 225–253.

Ionic radii follow the same vertical trend as atomic radii; That is, for ions with the same charge, going down a column, the ionic radius increases. The reason is the same as with atomic rays: the shielding of the filled inner shells causes only a small change in the effective nuclear charge, which is perceived by the outermost electrons. Again, the main layers with higher values ​​ofnorteThey are located at increasing distances from the nucleus.

As elements in different columns tend to form ions with different charges, it is not possible to compare ions of the same charge in a row of the periodic table. Instead, because of their different atomic numbers, adjacent elements tend to form ions with the same number of electrons but different overall charges. One such group of species is known asisoelectronic seriesA group of ions or atoms and ions that have the same number of electrons and therefore the same electronic configuration in the ground state.. For example, the isoelectronic series of species with the neon closed shell configuration (1S22S22Page6) is displayed inTable 7.3 “Radius of ions with closed shell neon electron configuration”. The sizes of the ions in this series steadily decrease from N3-in Al3+. The six ions contain 10 electrons in the firstS, 2S, e 2Pageorbitals, but the nuclear charge ranges from +7 (N) to +13 (Al). If the positive charge of the nucleus increases while the number of electrons remains the same, there is greater electrostatic attraction between the electrons and the nucleus, causing the radius to decrease. Consequently, the ion with the highest nuclear charge (Al3+) is the smallest and the ion with the smallest nuclear charge (N3-) He is taller. A member of this isoelectronic series is not listed inTable 7.3 “Radius of ions with closed shell neon electron configuration”: the neon atom. As neon does not form ionic or covalent bonds, its radius is difficult to measure.

Table 7.3Ionic radius with the closed shell electron configuration of neon

Pure Radio (afternoon) atomic number
norte3- 146 7
Ö2- 140 8
F 133 9
Von+ 102 11
Magnesium2+ 72 12
Alabama3+ 53,5 13

Quelle: R. D. Shannon, „Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides“crystallographic record32, nº. 5 (1976): 751-767.

Example 3

Arrange these ions in order of increasing radius based on their positions in the periodic table: Cl, k+, S2-, E2-.

Given:four ions

At the request of:sort by increasing radius


ADetermine which ions form an isoelectronic series. From these ions, predict their relative sizes based on their nuclear charges. For ions that do not form an isoelectronic series, find their positions in the periodic table.

BDetermine the relative sizes of ions using their principal quantum numbersnorteand their positions within a series.


AWe see that S and Cl are to the right of the third row, while K and Se are to the left and right of the fourth row, respectively. What+, Kl, e S2-form an isoelectronic series with the shell-closed electron configuration [Ar]; That is, the three ions contain 18 electrons but have different nuclear charges. Because what+has the highest nuclear charge (Z=19), its radius is the smallest and S2-swindlerZ=16 has the largest radius. Since selenium is directly below sulfur, we expect Se2-Ion is even bigger than S2-.BSo the order must be K+<Cl<S2-<Se2-.

a practice

Arrange these ions in order of increasing size according to their position on the periodic table: Br, California2+, Rb+, e Sr.2+.



A variety of methods have been developed to measure the size of a single atom or ion. Hekovalenter Atomradius (Rto be)is half the nuclear distance in a molecule with two identical atoms bonded while themetallic atomic radius (Rmeet)is defined as half the distance between the nuclei of two adjacent atoms in a metallic element. HeRadio de van der Waals (RvdW)of an element is half the internuclear distance between two unbonded atoms in a solid. Atomic radii decrease from left to right along a line as the effective nuclear charge increases due to poor recognition of electrons by other electrons in the same parent shell. Also, the atomic radii in a column increase from top to bottom because the effective nuclear charge remains relatively constant as the principal quantum number increases. Heionic raysof cations and anions are always smaller and larger than the parent atom, respectively, due to changes in electron-electron repulsion, and trends in ionic radius parallel those in atomic size. A comparison of the dimensions of atoms or ions that have the same number of electrons but different nuclear charges is called aisoelectronic series, shows a clear correlation between increasing nuclear charge and decreasing size.

main point

  • Ionic radii share the same vertical trend as atomic radii, but the horizontal trends differ due to differences in ionic charges.

conceptual problems

  1. The electrons of 1SThe shells have a stronger electrostatic attraction to the nucleus than the electrons in the 2ndSmango. Give two reasons for this.

  2. Predict whether Na or Cl has the most stable 1S2Peel and explain your reasoning.

  3. Order K, F, Ba, Pb, B and I by decreasing the atomic radius.

  4. Sort Ag, Pt, Mg, C, Cu and Si by increasing the atomic radius.

  5. Using the periodic table, arrange Li, Ga, Ba, Cl, and Ni in order of increasing atomic radius.

  6. Element M is a metal that forms MX-type compounds.2, MX3e MX4, where X is a halogen. What is the expected trend of the ionic radius of M in these compounds? Arrange these compounds in order of decreasing ionic radius of M.

  7. The atomic radii of Na and Cl are 190 and 79 pm, respectively, but the distance between sodium and chlorine in NaCl is 282 pm. Explain this discrepancy.

  8. Are the shielding effects on atomic rays more pronounced in a row or in a group? Why?

  9. What two factors affect the size of an ion relative to the size of its parent atom? Wait for the ionic radius of S2-be the same in MgS and Na2S? Why or why not?

  10. get a brother, Al3+, Sir2+, F, Oh2-, Me tooin order of increasing ionic radius.

  11. organize3-, geek3-, Kl, Em3+, e S2-decreasing ionic radius order.

  12. How does an isoelectronic series differ from a series of ions of the same charge? Do magnesium, strontium, and potassium sulfate cations form an isoelectronic series? Why or why not?

  13. Which isoelectronic series arises from fluorine, nitrogen, magnesium, and carbon? Arrange the ions in this order

    1. increasing to nuclear charge.
    2. growing size
  14. What would be the charge and electron configuration of an isoelectronic calcium ion?

    1. a chloride ion?
    2. Arkansas+?
(Video) Ionic Radius Trends, Basic Introduction, Periodic Table, Sizes of Isoelectric Ions, Chemistry


  1. die 1SThe shell is closer to the core and therefore experiences greater electrostatic attraction. In addition, the electrons of the 2ndSBottom casing are protected by padding 1S2Layer that further reduces the electrostatic attraction to the core.

  2. Ba > K > Pb > I > B > F

  3. The sum of the calculated atomic radii of sodium and chlorineAtomIt's 253 hours. The sodium cation is significantly smaller than a neutral sodium atom (102 vs. 154 pm), which can be attributed to the loss of the single electron at 3Sorbital. In contrast, the chloride ion is much larger than a neutral chlorine atom (181 vs. 99 pm) because the added electron results in a much greater electron-electron repulsion within the filled atom.norte=3 main shield. Therefore, transferring an electron from sodium to chlorine reduces the radius of sodium by about 50%, but causes the radius of chlorine to nearly double. The net effect is that is the distance between a sodium ion and a chloride ion in NaClBigger thenthan the sum of the atomic radii of neutral atoms.

numerical problems

  1. Plot ionic charge versus ionic radius using the following data for Mo: Mo3+, 69 S.M.; Lun4+, 65 hours; And mo5+, 61h. Then use this graph to predict the ionic radius of Mo6+. Is the observed trend consistent with the general trends discussed in this chapter? Why or why not?

  2. Internuclear distances for selected ionic compounds are given in the table below.

    1. If the ionic radius of Li+is 76 pm, what is the ionic radius of the individual anions?

      LiF LiCl LiBr of
      distance (pm) 209 257 272 296
      (Video) Periodic Trends: Electronegativity, Ionization Energy, Atomic Radius - TUTOR HOTLINE
    2. What is the ionic radius of Na?+?

      NaF NaCl NaBr NaI
      distance (pm) 235 282 298 322
  3. Classify the gas species Mg2+, PAG3-, Brother, S2-, F, e n3-in increasing radius and justify your decisions.


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5. Periodic Trends: Ionic Radius (Ionic Size) | Study Chemistry With Us
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