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learning goals
- Understand periodic trends in atomic radii.
- Prediction of 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.
atomic radius
Remember that the probability of finding an electron in the various available orbitals slowly decreases as distance from the nucleus increases. This point is illustrated in Figure 2.8.1, which plots 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 2.8.1 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 in a given diagram corresponds to the density of electrons in a given main shell. Since helium has only one filled shell (norte= 1), shows a single peak. In contrast, neon, full ofnorte= 1 and 2 main shells, has two peaks. Argon, full ofnorte= 1, 2 and 3 main shells, has three points. The summit of fillingsnorte= 1 projectile occurs at shorter and shorter intervals for neon (Z= 10) and argon (Z= 18) because their nuclei are more positively charged than helium with the highest number of protons. why the 1S2layer closest to the nucleus, its electrons are very poorly shielded by electrons in filled shells with higher values ofnorte. Consequently, the two electrons in thenorte= 1 layer experiences almost full nuclear charge, resulting in a strong electrostatic interaction between the electrons and the nucleus. the energy ofnorte= 1 bowl also decreases a lot (the 1 fullSorbital becomes more stable) as the nuclear charge increases. For similar reasons, fillingnorte= 2 shell in argon is closer to the nucleus and has less energy than thatnorte= 2 neon bowls.
Figure 2.8.1 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 sizes of atoms. For example, the internuclear distance in diatomic Cl2The molecule is known to be 198 pm. We assign half this distance to each chlorine atom, giving chlorine a covalent atomic radius (RThat's it), which is half the distance between the nuclei of two identical atoms held together by a covalent bond in the same molecule,of 99 pm or 0.99 Å (part (a) in Figure 2.8.2).Atomic radii are usually measured in angstroms (Å), a non-SI unit: 1 Å = 1 × 10−10m = 100 hours.
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 formed between different elements by adding them together. For example, we could predict a carbon-chlorine distance of 77 pm + 99 pm = 176 pm for a C-Cl bond, 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. For example, for a metal, the metallic atomic radius (rmeeting) is defined as half the distance between the nuclei of two adjacent metal atoms (part (b) in Figure 2.8.2). For elements such as noble gases, many of which do not form stable compounds, we can use the so-called van der Waals atomic radius (rvdW), which is half the internuclear distance between two unbonded atoms in the solid (part (c) in Figure 2.8.2). This is rather difficult for helium, which does not form a solid at any temperature. An atom like chlorine has a covalent radius (the distance between two atoms in a molecule \(Cl_2\)) and a van der Waals radius (the distance between two Cl atoms in different molecules in, say, \(Cl_ {2 (s)}\) at low temperatures). These radii are usually not equal (part (d) in Figure 2.8.2).
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 devised a consistent method for calculating atomic radii using functions of quantum mechanics. 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 2.8.3). . ).
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 are in the upper right corner (Figure 2.8.4).
to use
Atomic radii decrease from left to right in a row (a period) and increase from top to bottom in a column (a group or family).
Trends in atomic size result from differences ineffective atomic charge (ZIt is made)experienced by electrons in the outermost orbitals of elements. For all elements except H, the effective nuclear charge is alwaysany 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. They all have a full 1S2inner hull, but as we move along the line from left to right, the core charge increases from +3 to +10. Although electrons are added to the secondSy 2PAGOrbital,Electrons in the same main shell are not very effective at shielding each other from nuclear charge.. Single 2 also diesSThe 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.) Both 2SThe electrons in beryllium don't shield each other very well, although the filled 1sS2Shell effectively neutralizes two of the four positive charges in the core. This means that the effective nuclear charge of the secondSThe electrons in beryllium oscillate between +1 and +2 (the calculated value is +1.66). Consequently, beryllium is significantly smaller than lithium. Likewise, as the series progresses, the increasing nuclear charge is not effectively neutralized by the electrons added to 2Sy 2PAGorbitals The result is a constant increase in effective nuclear charge and a constant decrease in atomic size.
The increase in atomic size along a column is also due to the shielding of electrons, but the situation is more complex due to the principal quantum number.norteis not constant As we saw in Chapter 2, the size of orbitals increasesnorteincreases,Assuming the nuclear charge remains the same. For example, in Group 1, the size of atoms increases significantly in the column. At first, it may seem reasonable to attribute this effect to the successive accumulation 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 numbernorteincreased from 2 to 6, but core charge increased from +3 to +55!
As a result, rays from thelower electron orbitalsin cesium they are much smaller than in lithium, and the electrons in these orbitals experience a much greater nuclear attraction. This force depends on the effective nuclear charge experienced by the inner electrons. 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 cesium to electrons in the outermost or valence shell becauseThe 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 1S22S22PAG63S23PAG64S23D104PAG65S24D105PAG6shells, abbreviated as [Xe]5S24D105PAG6, which effectively neutralizes most of the 55 positive charges in the nucleus. The same dynamic is responsible for the constant increase in magnitude that is observed as we move through the other columns of the periodic table. The irregularities can usually be explained by variations in the effective nuclear charge.
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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 2.8.1
Arrange these elements in order of increasing atomic radii based on their positions on the periodic table: aluminum, carbon, and silicon.
Given:three elements
Asked:arrange by increasing atomic radius
Strategy:
- Identify the position of elements in the periodic table. Determine the relative sizes of elements that are in the same column from 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.
- Arrange the elements in order of increasing atomic radius.
Solution:
AThese items are not all in the same column or row, so we must 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.BThe combination of the two inequalities gives the general order: C < Si < Al.
Exercise 2.8.1
Arrange these elements in order of increasing magnitude based on their positions on the periodic table: oxygen, phosphorus, potassium, and sulfur.
- Responder:
- O < S < PAG < K
Ionic Radii and Isoelectronic Series
An ion is formed when one or more electrons are removed from a neutral atom (cation) to form a positive ion, or when additional electrons are attached to neutral atoms (anions) to form a negative one. The terms cation or anion come from early experiments with electricity, which found that positively charged particles are attracted to the negative terminal of a battery, the cathode, while negatively charged particles are attracted to the positive terminal, the anode.
Ionic compounds consist of regularly repeating arrangements of positively charged cations and negatively charged anions. While it is not possible to directly measure an ionic radius for the same reason, it is not possible to directly measure the radius of an atom.EsIt is possible to measure the distance between the nuclei of a cation and a neighboring anion in an ionic compound to determine the ionic radius (the radius of a cation or anion) of one or both. As shown in Figure 2.8.6, the core spacing corresponds to thattotalthe 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 returns slightly different values. For example, the radius of Na+The ion is essentially the same in NaCl and Na2S provided the same measurement method is used. Despite small methodological differences, certain trends can be observed.
A comparison of ionic radii with atomic radii (Figure 2.8.7)A cation that has lost an electron is always smaller than its neutral parent, and an anion that has gained an electron is always larger than its neutral parent.. 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 core. Consequently, the size of the region of space occupied by electrons decreases (compare Li at 167 pm with Li+at 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 h). On the other hand, adding one or more electrons to a neutral atom leads to an increase in electron-electron repulsion and a decrease in the effective nuclear charge, thus increasing the size of the probability region (compare F at 42 pm with F−at 1:33 p.m.).
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the cations areAlwayssmaller than the neutral atom, and are anionsAlwaysbigger than.
Since most elements form either a cation or an anion, but not both, there are few ways to compare the sizes of a cation and anion that come from the same neutral atom. However, some sodium compounds contain Na−ion, allowing its size to be compared with the much better known Na+ion found inmanylinks. The radius of sodium in each of its three known oxidation states is given in Table 2.8.1. All three types have a nuclear charge of +11, but contain 10 (Na+), 11 (Na0)y 12 (Na−) electrons. then a+The ion is significantly smaller than the neutral Na atom because the thirdS1The electron has been removed to give a closed shell withnorte= 2. The after−ion is larger than the Na atom because the extra electron creates a 3S2valence electron configuration while the nuclear charge remains the same.
| Of+ | Of0 | Of− | |
|---|---|---|---|
| electronic configuration | 1S22S22PAG6 | 1S22S22PAG63S1 | 1S22S22PAG63S2 |
| Radio (afternoon) | 102 | 154* | 202† |
| *Metal radius measured for Na(s). | |||
| †Quelle: M. J. Wagner und J. L. Dye, „Alkalides, Electrides, and Expanded Metals“, Annual Review of Materials Science 23 (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 main shells with values greater thannorteThey are at increasing distances from the core.
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, neighboring elements tend to form ions with the same number of electrons but different total charges. Such a group of species is called an isoelectronic series. For example, the isoelectronic series of species with neon closed shell configuration (1S22S22PAG6) is shown in Table 7.3
The sizes of the ions in this series steadily decrease from N3-um Al3+. The six ions contain 10 electrons in the first one.S, 2S, e 2PAGorbitals, 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 a greater electrostatic attraction between the electrons and the nucleus, resulting in a reduction in radius. Consequently, the ion with the highest nuclear charge (Al3+) is the smallest and the ion with the smallest nuclear charge (N3-) It's the biggest. The neon atom in this isoelectronic series is not included in Table 2.8.3 because neon does not form covalent or ionic bonds and therefore its radius is difficult to measure.
| Pure | Radio (afternoon) | atomic number |
|---|---|---|
| norte3- | 146 | 7 |
| o2- | 140 | 8 |
| F− | 133 | 9 |
| Of+ | 98 | 11 |
| milligrams2+ | 79 | 12 |
| Alabama3+ | 57 | 13 |
Example 2.8.2
Arrange these ions according to their positions in the periodic table in order of increasing radius: Cl−, k+, S2-, and you are2-.
Given:four ions
Asked:Sort by increasing radius
Strategy:
- Determine 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.
- Determine the relative sizes of ions using their principal quantum numbersnorteand their positions within a series.
Solution:
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 closed-shell 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 even larger than S2-.BSo the order must be K+<Kl−<S2-<Se2-.
Exercise 2.8.2
Arrange these ions in order of increasing size based on their position in the periodic table: Br−, California2+, Rb+, e Sr.2+.
- Responder:
- California2+<Sr2+<Rb+<br−
Summary
Ionic radii share the same vertical trend as atomic radii, but the horizontal trends differ due to differences in ionic charges.
A variety of methods have been developed to measure the size of a single atom or ion. Hecovalent atomic radius (RThat's it)is half the internuclear distance in a molecule with two identical atoms bonded duringmetallic atomic radius (Rmeeting)is defined as half the distance between the nuclei of two adjacent atoms in a metallic element. HeRadio the 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 shielding of electrons by other electrons in the same parent shell. Also, atomic radii increase from top to bottom in a column 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 inisoelectronic series, shows a clear correlation between increasing nuclear charge and decreasing size.
Credits and Attributions
Adapted fromJoshua Halpern(Howard University)