Which List Correctly Gives Atoms In Order Of Increasing Size?

Chapter 3.2: Sizes of Atoms and Ions

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Learning Objectives

To understand periodic trends in atomic radii.

Although some people fall into the trap of visualizing atoms and ions equally small, difficult spheres similar to miniature table-tennis assurance or marbles, the breakthrough mechanical model tells u.s. that their shapes and boundaries are much less definite than those images suggest. Every bit a result, atoms and ions cannot be said to take exact sizes. In this department, we discuss how diminutive and ion "sizes" are divers and obtained.

Atomic Radii

Remember that the probability of finding an electron in the various available orbitals falls off slowly as the distance from the nucleus increases. This signal is illustrated in Effigy 3.2.1 which shows a plot of total electron density for all occupied orbitals for three noble gases equally a function of their distance from the nucleus. Electron density diminishes gradually with increasing distance, which makes it impossible to draw a precipitous line mark the boundary of an cantlet.

Graph of radial probability versus distance from the nucleus in picometers. 1s, 2s, and 2p for Argon have the highest probability, followed by 1s, 2s, and 2p for Neon, and finally 1s for Helium.

Effigy 3.ii.1 Plots of Radial Probability as a Function of Distance from the Nucleus for He, Ne, and Ar. In He, the ones electrons have a maximum radial probability at ≈thirty pm from the nucleus. In Ne, the 1s electrons take a maximum at ≈viii pm, and the 2s and 2p electrons combine to form another maximum at ≈35 pm (the n = 2 shell). In Ar, the is electrons have a maximum at ≈2 pm, the 2due south and twop electrons combine to form a maximum at ≈eighteen pm, and the 3southward and 3p electrons combine to form a maximum at ≈70 pm.

Figure 3.2.i too shows that in that location are distinct peaks in the total electron density at particular distances and that these peaks occur at different distances from the nucleus for each chemical element. Each meridian in a given plot corresponds to the electron density in a given chief shell. Because helium has but one filled shell (n = 1), information technology shows only a unmarried peak. In contrast, neon, with filled due north = one and 2 primary shells, has two peaks. Argon, with filled n = ane, 2, and 3 principal shells, has three peaks. The elevation for the filled north = one shell occurs at successively shorter distances for neon (Z = 10) and argon (Z = xviii) considering, with a greater number of protons, their nuclei are more positively charged than that of helium. Because the 1s ⁱⁱ trounce is closest to the nucleus, its electrons are very poorly shielded past electrons in filled shells with larger values of northward. Consequently, the ii electrons in the n = ane shell experience nearly the full nuclear accuse, resulting in a strong electrostatic interaction between the electrons and the nucleus. The energy of the n = 1 crush too decreases tremendously (the filled ones orbital becomes more stable) as the nuclear charge increases. For similar reasons, the filled n = two shell in argon is located closer to the nucleus and has a lower energy than the n = two vanquish in neon.

Figure 3.2.1 illustrates the difficulty of measuring the dimensions of an individual atom. Because distances between the nuclei in pairs of covalently bonded atoms tin exist measured quite precisely, however, chemists employ these distances as a basis for describing the approximate sizes of atoms. For example, the internuclear altitude in the diatomic Cl₂ molecule is known to be 198 pm. Nosotros assign half of this distance to each chlorine cantlet, giving chlorine a covalent atomic radius (r _cov), which is half the altitude between the nuclei of two like atoms joined by a covalent bond in the aforementioned molecule, of 99 pm or 0.99 Å (part (a) in Effigy iii.2.2). Atomic radii are ofttimes measured in angstroms (Å), a not-SI unit: 1 Å = one × 10^−x m = 100 pm.

Effigy 3.two.2 Definitions of the Atomic Radius. (a) The covalent atomic radius, r _cov, is half the distance between the nuclei of two similar atoms joined by a covalent bond in the same molecule, such as Cl_two. (b) The metallic atomic radius, r _met, is half the altitude between the nuclei of ii adjacent atoms in a pure solid metal, such as aluminum. (c) The van der Waals diminutive radius, r _vdW, is one-half the distance between the nuclei of two like atoms, such as argon, that are closely packed but not bonded. (d) This is a depiction of covalent versus van der Waals radii of chlorine. The covalent radius of Cl₂ is the altitude between the two chlorine atoms in a unmarried molecule of Cl_two. The van der Waals radius is the distance betwixt chlorine nuclei in 2 different simply touching Cl₂ molecules. Which practise you think is larger? Why?

In a like arroyo, we tin use the lengths of carbon–carbon single bonds in organic compounds, which are remarkably compatible at 154 pm, to assign a value of 77 pm every bit the covalent atomic radius for carbon. If these values practice indeed reflect the actual sizes of the atoms, then we should be able to predict the lengths of covalent bonds formed betwixt unlike elements past adding them. For case, we would predict a carbon–chlorine distance of 77 pm + 99 pm = 176 pm for a C–Cl bail, which is very close to the average value observed in many organochlorine compounds.A similar approach for measuring the size of ions is discussed afterwards in this department.

Covalent diminutive radii can be determined for nearly of the nonmetals, merely how practise chemists obtain diminutive radii for elements that do not form covalent bonds? For these elements, a multifariousness of other methods accept been adult. With a metal, for example, the metallic atomic radius(r _met) is divers as one-half the distance between the nuclei of two adjacent metallic atoms (role (b) in Figure 3.2.2). For elements such every bit the noble gases, near of which grade no stable compounds, nosotros tin can apply what is chosen the van der Waals atomic radius (r _vdW), which is half the internuclear distance between ii nonbonded atoms in the solid (part (c) in Figure 3.2.2 ). This is somewhat difficult for helium which does not course a solid at any temperature. An atom such as chlorine has both a covalent radius (the distance between the two atoms in a Cl_ii molecule) and a van der Waals radius (the distance between ii Cl atoms in unlike molecules in, for example, Cl₂(s) at low temperatures). These radii are generally non the same (part (d) in Effigy three.2.ii ).

Periodic Trends in Diminutive Radii

Considering information technology is incommunicable to measure the sizes of both metallic and nonmetallic elements using any ane method, chemists have developed a self-consistent way of computing diminutive radii using the quantum mechanical functions described in Chapter 2. Although the radii values obtained by such calculations are not identical to any of the experimentally measured sets of values, they do provide a mode to compare the intrinsic sizes of all the elements and conspicuously evidence that atomic size varies in a periodic style (Effigy three.two.iii). In the periodic table, atomic radii decrease from left to right across a row and increase from top to bottom down a column. Because of these 2 trends, the largest atoms are establish in the lower left corner of the periodic tabular array, and the smallest are found in the upper right corner (Figure 3.2.4).

Graph of atomic number versus the calculated atomic radius in picometers for the s block, p block, and d block.

Figure 3.2.iii A Plot of Periodic Variation of Atomic Radius with Atomic Number for the Offset Six Rows of the Periodic Table. There is a similarity to the plot of atomic volume versus atomic number (Figure three.i.two )—a variation of Meyer'south early plot.

Figure 3.2.4 Calculated Diminutive Radii (in Picometers) of the due south-, p-, and d-Block Elements. The sizes of the circles illustrate the relative sizes of the atoms. The calculated values are based on breakthrough mechanical wave functions. Source: http://www.webelements.com. Web Elements is an splendid on line source for looking upwards diminutive properties. Visit the site.

Note the Pattern

Atomic radii subtract from left to correct across a row and increase from top to lesser down a column.

Trends in atomic size result from differences in the effective nuclear charges ( Z _eff ) experienced by electrons in the outermost orbitals of the elements. As we described in Chapter 2, for all elements except H, the constructive nuclear charge is always less than the actual nuclear charge because of shielding furnishings. The greater the effective nuclear accuse, the more strongly the outermost electrons are attracted to the nucleus and the smaller the atomic radius.

The atoms in the second row of the periodic table (Li through Ne) illustrate the event of electron shielding. All have a filled ones ² inner shell, but every bit nosotros become from left to right across the row, the nuclear accuse increases from +3 to +x. Although electrons are existence added to the 2s and twop orbitals, electrons in the same principal shell are non very constructive at shielding one some other from the nuclear accuse. Thus the single twosouthward electron in lithium experiences an effective nuclear charge of approximately +1 because the electrons in the filled 1south ² shell effectively neutralize two of the three positive charges in the nucleus. (More than detailed calculations give a value of Z _eff = +1.26 for Li.) In contrast, the two iidue south electrons in glucinium practice not shield each other very well, although the filled is ^two shell finer neutralizes two of the 4 positive charges in the nucleus. This means that the constructive nuclear accuse experienced by the iidue south electrons in beryllium is betwixt +1 and +2 (the calculated value is +ane.66). Consequently, glucinium is significantly smaller than lithium. Similarly, as nosotros proceed across the row, the increasing nuclear accuse is non effectively neutralized by the electrons being added to the 2southward and twop orbitals. The result is a steady increment in the effective nuclear charge and a steady decrease in atomic size.

Figure 3.2.v The Atomic Radius of the Elements. The atomic radius of the elements increases as we go from right to left across a period and as we go downwardly the periods in a grouping.

The increase in atomic size going downward a column is besides due to electron shielding, only the situation is more than complex considering the principal quantum number n is non abiding. As we saw in Affiliate 2, the size of the orbitals increases equally n increases, provided the nuclear charge remains the same. In group 1, for example, the size of the atoms increases substantially going down the column. It may at get-go seem reasonable to attribute this effect to the successive addition of electrons to ns orbitals with increasing values of due north. However, it is important to remember that the radius of an orbital depends dramatically on the nuclear charge. As we go down the column of the group one elements, the principal breakthrough number n increases from 2 to 6, merely the nuclear charge increases from +3 to +55!

As a consequence the radii of the lower electron orbitals in Cesium are much smaller than those in lithium and the electrons in those orbitals experience a much larger strength of attraction to the nucleus. That forcefulness depends on the constructive nuclear charge experienced by the the inner electrons. If the outermost electrons in cesium experienced the full nuclear charge of +55, a cesium atom would be very small indeed. In fact, the effective nuclear charge felt by the outermost electrons in cesium is much less than expected (6 rather than 55). This ways that cesium, with a 6s ¹ valence electron configuration, is much larger than lithium, with a 2s ⁱ valence electron configuration. The effective nuclear charge changes relatively little for electrons in the outermost, or valence shell, from lithium to cesium because electrons in filled inner shells are highly effective at shielding electrons in outer shells from the nuclear charge. Even though cesium has a nuclear charge of +55, information technology has 54 electrons in its filled is ⁱⁱ2s ^twoiip ⁶3south ²threep ⁶4s ²iiid ^ten4p ⁶fives ²4d ^xfivep ⁶ shells, abbreviated as [Xe]fivesouthward ²4d ¹⁰5p ⁶, which effectively neutralize well-nigh of the 55 positive charges in the nucleus. The same dynamic is responsible for the steady increase in size observed as we go downward the other columns of the periodic table. Irregularities can usually exist explained by variations in effective nuclear charge.

Note the Blueprint

Electrons in the same main trounce are not very effective at shielding i another from the nuclear accuse, whereas electrons in filled inner shells are highly effective at shielding electrons in outer shells from the nuclear accuse.

Example 3.2.1

On the ground of their positions in the periodic table, adjust these elements in order of increasing diminutive radius: aluminum, carbon, and silicon.

Given: three elements

Asked for: arrange in gild of increasing diminutive radius

Strategy:

A Identify the location of the elements in the periodic tabular array. Make up one's mind the relative sizes of elements located in the same column from their principal quantum number n. Then decide the gild of elements in the same row from their effective nuclear charges. If the elements are non in the same cavalcade or row, use pairwise comparisons.

B List the elements in order of increasing atomic radius.

Solution:

A These elements are not all in the aforementioned column or row, so we must use pairwise comparisons. Carbon and silicon are both in group xiv with carbon lying in a higher place, so carbon is smaller than silicon (C < Si). Aluminum and silicon are both in the third row with aluminum lying to the left, then silicon is smaller than aluminum (Si < Al) because its effective nuclear accuse is greater. B Combining the 2 inequalities gives the overall society: C < Si < Al.

Exercise

On the basis of their positions in the periodic table, arrange these elements in order of increasing size: oxygen, phosphorus, potassium, and sulfur.

Answer: O < South < P < G

Ionic Radii and Isoelectronic Series

An ion is formed when either 1 or more electrons are removed from a neutral atom (cations) to form a positive ion or when additional electrons attach themselves to neutral atoms (anions) to form a negative one. The designations cation or anion come from the early experiments with electricity which found that positively charged particles were attracted to the negative pole of a bombardment, the cathode, while negatively charged ones were attracted to the positive pole, the anode.

Ionic compounds consist of regular repeating arrays of alternating positively charged cations and negatively charges anions. Although it is not possible to measure an ionic radius directly for the same reason information technology is not possible to direct measure an atom's radius, information technology is possible to measure the altitude between the nuclei of a cation and an next anion in an ionic chemical compound to determine the ionic radius (the radius of a cation or anion) of one or both. Every bit illustrated in Figure 3.ii.6 , the internuclear distance corresponds to the sum of the radii of the cation and anion. A diversity of methods have been developed to divide the experimentally measured distance proportionally between the smaller cation and larger anion. These methods produce sets of ionic radii that are internally consequent from one ionic chemical compound to another, although each method gives slightly unlike values. For example, the radius of the Na⁺ ion is essentially the same in NaCl and Na₂Southward, as long equally the same method is used to measure it. Thus despite minor differences due to methodology, certain trends can be observed.

Figure 3.2.six Definition of Ionic Radius. (a) The internuclear altitude is apportioned between adjacent cations (positively charged ions) and anions (negatively charged ions) in the ionic construction, as shown here for Na⁺ and Cl⁻ in sodium chloride. (b) This depiction of electron density contours for a single plane of atoms in the NaCl construction shows how the lines connect points of equal electron density. Notation the relative sizes of the electron density contour lines effectually Cl⁻ and Na⁺.

A comparison of ionic radii with atomic radii (Figure three.2.7) cation, having lost an electron, is always smaller than its parent neutral atom, and an anion, having gained an electron, is always larger than the parent neutral atom. When ane or more electrons is removed from a neutral atom, two things happen: (ane) repulsions between electrons in the same principal vanquish decrease because fewer electrons are present, and (two) the effective nuclear charge felt by the remaining electrons increases considering in that location are fewer electrons to shield one another from the nucleus. Consequently, the size of the region of space occupied by electrons decreases (compare Li at 167 pm with Li⁺ at 76 pm). If different numbers of electrons tin be removed to produce ions with different charges, the ion with the greatest positive accuse is the smallest (compare Fe² ⁺ at 78 pm with Fe³ ⁺ at 64.5 pm). Conversely, calculation 1 or more electrons to a neutral atom causes electron–electron repulsions to increase and the constructive nuclear charge to decrease, so the size of the probability region increases (compare F at 42 pm with F⁻ at 133 pm).

three.2.7 Ionic Radii (in Picometers) of the Nigh Common Ionic States of the s-, p-, and d-Cake Elements. Grey circles indicate the sizes of the ions shown; colored circles indicate the sizes of the neutral atoms, previously shown in Figure 3.vii . Source: Ionic radius data from R. D. Shannon, "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides," Acta Crystallographica 32, no. 5 (1976): 751–767.

Annotation the Design

Cations are always smaller than the neutral atom, and anions are e'er larger.

Considering most elements grade either a cation or an anion but non both, in that location are few opportunities to compare the sizes of a cation and an anion derived from the same neutral atom. A few compounds of sodium, however, contain the Na⁻ ion, allowing comparison of its size with that of the far more than familiar Na⁺ ion, which is establish in many compounds. The radius of sodium in each of its three known oxidation states is given in Table 3.2.ane. All iii species have a nuclear charge of +xi, just they contain x (Na⁺), 11 (Na⁰), and 12 (Na⁻) electrons. The Na⁺ ion is significantly smaller than the neutral Na atom considering the 3s ⁱ electron has been removed to give a airtight shell with n = 2. The Na⁻ ion is larger than the parent Na atom considering the additional electron produces a 3s ² valence electron configuration, while the nuclear accuse remains the same.

Table iii.2.1 Experimentally Measured Values for the Radius of Sodium in Its Iii Known Oxidation States

	Na⁺	Na⁰	Na^-
Electron configuration	1sⁱⁱ2sⁱⁱ2p^six	1s^two2s²2p⁶3s^one	1s²2s^two2p⁶3s²
Radius (pm	102	154^*	202^*

* The metallic radius measured for Na
Source: M.J. Wagner and J.L. Dye "Alkalides, Electrides and Expanded Metals," Annual Review of Materials Scientific discipline 23 (1993) 225-253.

. The sizes of the ions in this series subtract smoothly from North³⁻ to Al³ ⁺. All six of the ions contain 10 electrons in the onesouthward, iis, and iip orbitals, but the nuclear charge varies from +7 (Northward) to +13 (Al). As the positive charge of the nucleus increases while the number of electrons remains the aforementioned, there is a greater electrostatic attraction between the electrons and the nucleus, which causes a subtract in radius. Consequently, the ion with the greatest nuclear accuse (Al³ ⁺) is the smallest, and the ion with the smallest nuclear accuse (Northⁱⁱⁱ⁻) is the largest. 1 member of this isoelectronic series is non listed in Table iii.2.three : the neon cantlet. Because neon forms no covalent or ionic compounds, its radius is difficult to measure out.

Ion	Radius (pm)	Atomic Number
N³⁻	146	7
O²⁻	140	viii
F⁻	133	9
Na⁺	98	11
Mg² ⁺	79	12
Al³ ⁺	57	thirteen

Table iii.ii.3 Radius of Ions with the Neon Closed-Shell Electron Configuration. Source: R. D. Shannon, "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides," Acta Crystallographica 32, no. v (1976): 751–767.

Case 3.two.2

Based on their positions in the periodic tabular array, conform these ions in gild of increasing radius: Cl⁻, G⁺, Due south²⁻, and Seⁱⁱ⁻.

Given: four ions

Asked for: gild by increasing radius

Strategy:

A Determine which ions form an isoelectronic serial. Of those ions, predict their relative sizes based on their nuclear charges. For ions that do not form an isoelectronic serial, locate their positions in the periodic table.

B Determine the relative sizes of the ions based on their principal quantum numbers n and their locations within a row.

Solution:

A We run into that Due south and Cl are at the right of the tertiary row, while K and Se are at the far left and right ends of the 4th row, respectively. K⁺, Cl⁻, and S^two− form an isoelectronic series with the [Ar] closed-shell electron configuration; that is, all iii ions incorporate 18 electrons but have different nuclear charges. Because M⁺ has the greatest nuclear accuse (Z = 19), its radius is smallest, and Southⁱⁱ⁻ with Z = 16 has the largest radius. Because selenium is directly below sulfur, nosotros expect the Se²⁻ ion to be even larger than S^two−. B The order must therefore be K⁺ < Cl⁻ < Southⁱⁱ⁻ < Se²⁻.

Exercise

Based on their positions in the periodic table, arrange these ions in order of increasing size: Br⁻, Caⁱⁱ ⁺, Rb⁺, and Srⁱⁱ ⁺.

Respond: Ca^two ⁺ < Sr² ⁺ < Rb⁺ < Br⁻

Summary

A variety of methods have been established to measure the size of a single atom or ion. The covalent atomic radius ( r _cov ) is half the internuclear distance in a molecule with two identical atoms bonded to each other, whereas the metallic atomic radius ( r _met ) is defined as half the distance between the nuclei of two adjacent atoms in a metallic element. The van der Waals radius ( r _vdW ) of an chemical element is half the internuclear distance betwixt two nonbonded atoms in a solid. Atomic radii decrease from left to right across a row considering of the increase in effective nuclear accuse due to poor electron screening by other electrons in the same principal shell. Moreover, atomic radii increase from tiptop to bottom down a column considering the effective nuclear charge remains relatively constant as the principal breakthrough number increases. The ionic radii of cations and anions are always smaller or larger, respectively, than the parent atom due to changes in electron–electron repulsions, and the trends in ionic radius parallel those in atomic size. A comparison of the dimensions of atoms or ions that have the aforementioned number of electrons only dissimilar nuclear charges, called an isoelectronic series, shows a clear correlation betwixt increasing nuclear charge and decreasing size.

Fundamental Takeaway

Ionic radii share the aforementioned vertical tendency as atomic radii, merely the horizontal trends differ due to differences in ionic charges.

Conceptual Problems

The electrons of the isouth vanquish have a stronger electrostatic attraction to the nucleus than electrons in the iisouth beat out. Give two reasons for this.
Predict whether Na or Cl has the more stable 1s ² beat out and explain your rationale.
Arrange K, F, Ba, Pb, B, and I in order of decreasing atomic radius.
Adapt Ag, Pt, Mg, C, Cu, and Si in society of increasing atomic radius.
Using the periodic table, arrange Li, Ga, Ba, Cl, and Ni in order of increasing atomic radius.
Element Thousand is a metallic that forms compounds of the type MX_two, MX_iii, and MX₄, where X is a halogen. What is the expected trend in the ionic radius of One thousand in these compounds? Conform these compounds in order of decreasing ionic radius of M.
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. Explicate this discrepancy.
Are shielding effects on the atomic radius more pronounced across a row or down a group? Why?
What 2 factors influence the size of an ion relative to the size of its parent atom? Would you lot expect the ionic radius of Sⁱⁱ⁻ to be the aforementioned in both MgS and Na_iiS? Why or why not?
Arrange Br⁻, Alⁱⁱⁱ ⁺, Sr² ⁺, F⁻, O^two−, and I⁻ in order of increasing ionic radius.
Conform Pⁱⁱⁱ⁻, N³⁻, Cl⁻, In³ ⁺, and Due south²⁻ in order of decreasing ionic radius.
How is an isoelectronic serial different from a serial of ions with the aforementioned charge? Exercise the cations in magnesium, strontium, and potassium sulfate form an isoelectronic series? Why or why not?
What isoelectronic series arises from fluorine, nitrogen, magnesium, and carbon? Adapt the ions in this serial by
1. increasing nuclear charge.
2. increasing size.
What would be the charge and electron configuration of an ion formed from calcium that is isoelectronic with
1. a chloride ion?
2. Ar⁺?

Answers

The 1s vanquish is closer to the nucleus and therefore experiences a greater electrostatic attraction. In addition, the electrons in the 2southward subshell are shielded by the filled 1s ² crush, which farther decreases the electrostatic attraction to the nucleus.
Ba > K > Pb > I > B > F
The sum of the calculated diminutive radii of sodium and chlorine atoms is 253 pm. The sodium cation is significantly smaller than a neutral sodium atom (102 versus 154 pm), due to the loss of the single electron in the 3s orbital. Conversely, the chloride ion is much larger than a neutral chlorine atom (181 versus 99 pm), because the added electron results in greatly increased electron–electron repulsions within the filled north = 3 chief beat out. Thus, transferring an electron from sodium to chlorine decreases the radius of sodium by about 50%, but causes the radius of chlorine to almost double. The net upshot is that the distance between a sodium ion and a chloride ion in NaCl is greater than the sum of the atomic radii of the neutral atoms.

Numerical Problems

Plot the ionic charge versus ionic radius using the post-obit data for Mo: Moⁱⁱⁱ ⁺, 69 pm; Mo^four ⁺, 65 pm; and Mo⁵ ⁺, 61 pm. Then use this plot to predict the ionic radius of Mo^vi ⁺. Is the observed trend consistent with the full general trends discussed in the chapter? Why or why not?

Internuclear distances for selected ionic compounds are given in the post-obit table.

If the ionic radius of Li⁺ is 76 pm, what is the ionic radius of each of the anions?

	LiF	LiCl	LiBr	LiI
Altitude (pm)	209	257	272	296

What is the ionic radius of Na⁺?

	NaF	NaCl	NaBr	NaI
Distance (pm)	235	282	298	322

Arrange the gaseous species Mgⁱⁱ ⁺, P³⁻, Br⁻, S²⁻, F⁻, and N^three− in social club of increasing radius and justify your decisions.

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Modified past Joshua Halpern