[{"data":1,"prerenderedAt":203},["ShallowReactive",2],{"topic-periodic-properties-and-trends":3},{"topic":4,"prev":189,"next":195},{"id":5,"slug":6,"title":7,"shortTitle":8,"lesson":5,"category":9,"description":10,"metaDescription":11,"objectives":12,"conceptSections":31,"workedExample":91,"oerSources":101,"selfStudyQuestions":105,"relatedTopicSlugs":134,"relatedElements":138,"relatedReferences":146,"keyEquations":147,"howTo":156,"conceptProbe":165,"practiceTeaser":169,"gatedContent":176,"seoKeywords":179,"lastAlignmentAudit":187,"objectiveCount":188},13,"periodic-properties-and-trends","Periodic Properties and Trends","Periodic Trends","atomic-structure","Read the periodic table as a predictive tool: valence electrons, atomic and ionic radius, ionization energy, electronegativity, electron affinity, and using trends to predict ionic vs covalent bonding.","Periodic trends explained: valence electrons, atomic and ionic radius, ionization energy, electronegativity, electron affinity, and predicting ionic vs covalent bonding.",[13,16,19,22,25,28],{"id":14,"text":15},"13.1","Predict relative atomic radii from periodic position across periods and down groups",{"id":17,"text":18},"13.2","Predict relative ionization energies from periodic position and identify the major trend exceptions (Be → B, N → O)",{"id":20,"text":21},"13.3","Compare electronegativity and electron affinity values across elements using periodic trends",{"id":23,"text":24},"13.4","Compare the radius of an ion to its parent atom (cation \u003C parent; anion > parent) and apply the rule to specific cases",{"id":26,"text":27},"13.5","Rank isoelectronic species by ionic radius",{"id":29,"text":30},"13.6","Use periodic trends and valence patterns to identify elements with similar properties and predict whether element combinations are more likely to form ionic or covalent bonds",[32,37,47,55,64,73,82,87],{"heading":33,"content":34,"relatedObjectives":35},"Valence Electrons and the Periodic Table","\u003Cp>\u003Cem>Note on topic scope:\u003C/em> \u003Cstrong>This topic (T13) covers periodic properties and trends\u003C/strong> — using the periodic table to predict atomic and ionic size, ionization energy, electronegativity, electron affinity, and bond-type tendencies. If you need to write or interpret electron configurations, start with \u003Cstrong>T12: \u003Ca href=\"/learn/electron-structure-and-light\">Electron Structure and Light\u003C/a>\u003C/strong>; come back here to reason about how those configurations drive periodic patterns.\u003C/p>\u003Cp>\u003Cstrong>Valence electrons\u003C/strong> are the electrons in the outermost energy level (highest n value) of an atom. They are the electrons that participate in bonding and chemical reactions, and they determine an element’s chemistry.\u003C/p>\u003Cul>\u003Cli>For \u003Cstrong>main-group elements\u003C/strong>, the number of valence electrons equals the column position within the s/p block. Group 1 has 1 valence electron (ns¹); Group 2 has 2 (ns²); Group 13 has 3 (ns² np¹); … Group 17 has 7 (ns² np⁵); Group 18 has 8 (ns² np⁶), except He which has 2.\u003C/li>\u003Cli>For \u003Cstrong>transition metals\u003C/strong>, both the ns and (n−1)d electrons can participate in chemistry, which is why transition metals show variable oxidation states.\u003C/li>\u003C/ul>\u003Cp>The periodic table is organized by electron configuration, which is what makes it predictive:\u003C/p>\u003Cul>\u003Cli>\u003Cstrong>s-block\u003C/strong> — Groups 1 and 2 (ns¹ and ns² configurations).\u003C/li>\u003Cli>\u003Cstrong>p-block\u003C/strong> — Groups 13–18 (ns² np¹ … ns² np⁶ configurations).\u003C/li>\u003Cli>\u003Cstrong>d-block\u003C/strong> — transition metals (filling the (n−1)d subshell).\u003C/li>\u003Cli>\u003Cstrong>f-block\u003C/strong> — lanthanides and actinides (filling the (n−2)f subshell).\u003C/li>\u003C/ul>\u003Cp>The \u003Cstrong>period number\u003C/strong> equals the highest principal quantum number of the valence electrons. This direct connection between table position and configuration means you can write any element’s configuration just by reading its position.\u003C/p>",[36],110,{"heading":38,"content":39,"relatedObjectives":40,"deepDive":43},"Effective Nuclear Charge and Shielding","\u003Cp>Every periodic trend comes back to a single tug-of-war: nuclear pull on valence electrons versus shielding by inner-shell electrons. The net pull on a specific electron is its \u003Cstrong>effective nuclear charge\u003C/strong>, Z\u003Csub>eff\u003C/sub>: the pull exerted on that electron by the nucleus, taking electron-electron repulsions into account. A useful approximation is Z\u003Csub>eff\u003C/sub> ≈ Z − (number of inner-shell electrons). Core electrons are adept at shielding, while electrons in the same valence shell do not block the nuclear attraction experienced by each other as efficiently.\u003C/p>\u003Cul>\u003Cli>\u003Cstrong>Across a period (left to right)\u003C/strong>: Z increases by 1 for each step, but the shielding from inner-shell electrons stays roughly constant. So Z\u003Csub>eff\u003C/sub> \u003Cem>increases\u003C/em> across a period — the nucleus pulls valence electrons more tightly.\u003C/li>\u003Cli>\u003Cstrong>Down a group (top to bottom)\u003C/strong>: each new period adds a full inner shell of electrons. The valence electrons sit in a higher shell, farther from the nucleus, with much more shielding. So Z\u003Csub>eff\u003C/sub> changes only modestly down a group, but the \u003Cem>distance\u003C/em> to the valence shell grows substantially.\u003C/li>\u003C/ul>\u003Cp>Three of the four periodic trends — atomic radius, ionization energy, electronegativity — follow directly from these two patterns. Memorizing the arrows is fine; the better skill is to reason through Z\u003Csub>eff\u003C/sub> + distance and let the answer fall out.\u003C/p>",[41,42],105,108,[44],{"label":45,"body":46},"One tug-of-war, every trend on this page","\u003Cp>Effective nuclear charge is the single mechanism behind this whole topic, so it pays to feel the arithmetic once. Sodium’s valence electron has 11 protons pulling it in, but 10 core electrons standing between, canceling most of that pull: Z\u003Csub>eff\u003C/sub> ≈ 11 − 10 = 1. Chlorine’s valence electrons, in that same third shell, sit behind only the same 10-electron core while 17 protons pull: Z\u003Csub>eff\u003C/sub> ≈ 7.\u003C/p>\u003Cp>Everything that follows: shrinking radii across a period, climbing ionization energies, rising electronegativity, is that one number changing. Master the tug-of-war and the trends stop being four facts to memorize and become one fact wearing four costumes.\u003C/p>",{"heading":48,"content":49,"relatedObjectives":50,"deepDive":51},"Atomic Radius","\u003Cp>\u003Cstrong>Atomic radius\u003C/strong> measures the size of an atom — typically the distance from the nucleus to the outermost electron shell.\u003C/p>\u003Cul>\u003Cli>\u003Cstrong>Across a period (left to right)\u003C/strong>: radius \u003Cstrong>decreases\u003C/strong>. Z\u003Csub>eff\u003C/sub> increases (more protons pulling), shielding stays roughly constant (same shell), so the valence electrons are pulled in closer.\u003C/li>\u003Cli>\u003Cstrong>Down a group (top to bottom)\u003C/strong>: radius \u003Cstrong>increases\u003C/strong>. Each new period adds a shell, which puts the outermost electrons farther from the nucleus.\u003C/li>\u003C/ul>\u003Cp>Examples:\u003C/p>\u003Cul>\u003Cli>Across period 3: Na > Mg > Al > Si > P > S > Cl (decreasing).\u003C/li>\u003Cli>Down group 1: Li < Na < K < Rb < Cs (increasing).\u003C/li>\u003C/ul>\u003Cp>To rank a mixed set of elements (e.g., Na vs Cl vs Cs), apply both rules: down-and-left is bigger; up-and-right is smaller. Cs is large (heavy alkali metal); Cl is small (right side, period 3); Na sits between them.\u003C/p>",[41],[52],{"label":53,"body":54},"Common mistake: more electrons means a bigger atom","\u003Cp>Moving from sodium to chlorine adds six electrons, so intuition says chlorine should be bigger. It is dramatically smaller. The added electrons enter the \u003Cem>same\u003C/em> third shell (no new layer of size), while the six added protons pull that whole shell inward with growing force. Size only jumps when a genuinely new shell opens, which happens down a group, not across a period.\u003C/p>\u003Cp>The corrected intuition: electron \u003Cem>count\u003C/em> does not set size; the number of occupied shells and the strength of the pull on the outermost one do. Across a period the shell count is fixed and the pull grows, so atoms shrink.\u003C/p>",{"heading":56,"content":57,"relatedObjectives":58,"deepDive":60},"Ionization Energy and Its Major Exceptions","\u003Cp>\u003Cstrong>Ionization energy (IE)\u003C/strong> is the energy required to remove the most loosely bound electron from a gaseous atom in its ground state: X(g) → X⁺(g) + e⁻. The first ionization energy (IE\u003Csub>1\u003C/sub>) removes the first electron; IE\u003Csub>2\u003C/sub>, IE\u003Csub>3\u003C/sub>, … remove subsequent electrons. Ionization processes are endothermic, so IE values are always positive.\u003C/p>\u003Cp>The general trend mirrors atomic radius (because closer-held electrons are harder to remove):\u003C/p>\u003Cul>\u003Cli>\u003Cstrong>Across a period\u003C/strong>: IE \u003Cstrong>increases\u003C/strong>. Higher Z\u003Csub>eff\u003C/sub>, smaller radius → harder to remove the valence electron.\u003C/li>\u003Cli>\u003Cstrong>Down a group\u003C/strong>: IE \u003Cstrong>decreases\u003C/strong>. Larger radius and more shielding → the outermost electron is loosely held.\u003C/li>\u003C/ul>\u003Cp>\u003Cstrong>Major exceptions.\u003C/strong> Two well-known dips break the smooth left-to-right increase across a period:\u003C/p>\u003Col>\u003Cli>\u003Cstrong>Group 13 vs Group 2\u003C/strong> (e.g., B < Be, Al < Mg). Group 13 starts the np subshell. Within any one shell, the s electrons are lower in energy than the p electrons, so an s electron is harder to remove than a p electron in the same shell. The first p electron is also shielded by the filled ns², so it leaves more easily than expected.\u003C/li>\u003Cli>\u003Cstrong>Group 16 vs Group 15\u003C/strong> (e.g., O < N, S < P). Group 15 has a half-filled np³ — an extra-stable arrangement. Removing one electron from the group-16 element eliminates the electron-electron repulsion caused by pairing electrons in a 2p orbital and leaves a half-filled p subshell (which is energetically favorable), so this electron leaves more easily than the smooth trend predicts.\u003C/li>\u003C/ol>\u003Cp>For \u003Cstrong>successive ionization energies\u003C/strong> (IE\u003Csub>1\u003C/sub>, IE\u003Csub>2\u003C/sub>, IE\u003Csub>3\u003C/sub>, …) of a single element, look for the large \u003Cstrong>jump\u003C/strong> when you start removing core electrons. Sc and Ga both have 3 valence electrons; both show a sharp increase in IE between IE\u003Csub>3\u003C/sub> and IE\u003Csub>4\u003C/sub> as the removal hits the noble-gas core. The position of the big jump tells you how many valence electrons the atom has.\u003C/p>",[42,59],109,[61],{"label":62,"body":63},"The giant leap that counts valence electrons","\u003Cp>Successive ionization energies are a valence-electron detector. Removing sodium’s first electron costs 496 kJ/mol; removing the second costs 4,562 kJ/mol, over nine times more, because the second electron must come out of the stable, closer-in core. For magnesium the giant leap arrives between IE₂ and IE₃; for aluminum, between IE₃ and IE₄.\u003C/p>\u003Cp>Read a table of successive ionization energies and the valence count announces itself: the cheap removals are valence electrons, and the wall is the core. This is direct experimental evidence for the shell structure you have been drawing since the Atomic Structure topic.\u003C/p>",{"heading":65,"content":66,"relatedObjectives":67,"deepDive":69},"Electronegativity and Electron Affinity","\u003Cp>Two more energy-related trends share the same direction as ionization energy:\u003C/p>\u003Cp>\u003Cstrong>Electronegativity (EN)\u003C/strong> is a relative scale of an atom’s tendency to \u003Cem>attract\u003C/em> shared electrons in a bond. The Pauling scale is the most common; values increase across a period and decrease down a group, for the same Z\u003Csub>eff\u003C/sub>-and-distance reasons that govern atomic radius and ionization energy. Fluorine has the highest electronegativity on the Pauling scale; the heavy alkali metals (Cs, Fr) are the lowest. EN is most useful as a way to predict bond polarity and bond-type tendency (see the LO 13.6 section below).\u003C/p>\u003Cp>\u003Cstrong>Electron affinity (EA)\u003C/strong> is the energy change when a gaseous atom gains an electron to form an anion: X(g) + e⁻ → X⁻(g). Conventionally a negative EA value means energy is released (exothermic), so “more negative EA” means “more eager to accept an electron.”\u003C/p>\u003Cul>\u003Cli>Across a period: EAs tend to become more negative (more exothermic) as Z\u003Csub>eff\u003C/sub> increases.\u003C/li>\u003Cli>Down a group: EAs tend to become less negative.\u003C/li>\u003Cli>Halogens have the most negative EA values (chlorine’s EA is −348 kJ/mol, the most negative of any element).\u003C/li>\u003Cli>Noble gases (group 18), group 2 elements, and group 15 (because of half-filled np³ stability) show \u003Cem>exceptions\u003C/em> to the trend — for these groups, adding an electron is much less favorable than the smooth left-to-right pattern would predict, because the incoming electron has to occupy a higher-energy subshell or pair against an existing half-filled p orbital.\u003C/li>\u003Cli>Counter-intuitively, fluorine’s EA (−328 kJ/mol) is \u003Cem>less\u003C/em> negative than chlorine’s, even though F is the most electronegative element. The reason is the very small n = 2 valence shell of fluorine: the incoming electron experiences strong electron-electron repulsion in the cramped 2p shell, which the larger 3p shell of chlorine avoids.\u003C/li>\u003C/ul>\u003Cp>The same Z\u003Csub>eff\u003C/sub> + distance reasoning that explained IE governs EN and EA as well. Think of the three (IE, EN, EA-magnitude) as one “hold on to electrons” trend with three different operational definitions.\u003C/p>",[68],107,[70],{"label":71,"body":72},"Common mistake: treating electronegativity and electron affinity as synonyms","\u003Cp>The names sound interchangeable; the concepts are not. Electron \u003Cem>affinity\u003C/em> is a measurable energy change: a lone gaseous atom captures an electron, and you can report the result in kJ/mol. Electro\u003Cem>negativity\u003C/em> is not measurable on any single atom: it is a relative, unitless scale (Pauling’s runs to about 4.0 at fluorine) describing how strongly an atom pulls on electrons it is \u003Cem>sharing in a bond\u003C/em>.\u003C/p>\u003Cp>The quick sort: no bond, real units, one atom → electron affinity. In a bond, no units, comparative → electronegativity. Both trend the same direction across the table, which is exactly why students merge them; keep the definitions separate and the exam questions untangle.\u003C/p>",{"heading":74,"content":75,"relatedObjectives":76,"deepDive":78},"Ionic Radius and Isoelectronic Species","\u003Cp>Forming an ion changes the size dramatically:\u003C/p>\u003Cul>\u003Cli>\u003Cstrong>Cations\u003C/strong> are \u003Cem>smaller\u003C/em> than their parent atoms. A cation has fewer electrons and the same number of protons as the parent atom, so it is smaller than the atom from which it is derived. As electrons are removed from the outer valence shell, the remaining core electrons (now occupying smaller shells) experience a greater effective nuclear charge Z\u003Csub>eff\u003C/sub> and are drawn even closer to the nucleus. Often a whole shell is lost: Al has a covalent radius of 118 pm; Al³⁺ has an ionic radius of 68 pm.\u003C/li>\u003Cli>\u003Cstrong>Anions\u003C/strong> are \u003Cem>larger\u003C/em> than their parent atoms. Adding electrons increases electron-electron repulsion and spreads the cloud out: a sulfur atom has a covalent radius of 104 pm, while the sulfide anion has an ionic radius of 170 pm.\u003C/li>\u003Cli>For cations of the same element with different charges, the higher charge gives the smaller ion: V²⁺ has an ionic radius of 79 pm versus V³⁺ at 64 pm.\u003C/li>\u003C/ul>\u003Cp>\u003Cstrong>Isoelectronic species\u003C/strong> are atoms and ions that have the same number of electrons (and therefore the same electron configuration). Examples include N³−, O²−, F−, Ne, Na⁺, Mg²⁺, and Al³⁺, which all have the Ne configuration, 1s²2s²2p⁶. The size rule for an isoelectronic series is simple: \u003Cem>more protons = smaller radius\u003C/em>. For the 10-electron series:\u003C/p>\u003Cp style=\"text-align:center;\">N³− (Z=7) > O²− (Z=8) > F− (Z=9) > Ne (Z=10) > Na⁺ (Z=11) > Mg²⁺ (Z=12) > Al³⁺ (Z=13)\u003C/p>\u003Cp>All seven species have the same [Ne] electron arrangement, but Al³⁺ has 13 protons pulling on those 10 electrons, while N³− has only 7. The size ranking is purely a Z\u003Csub>eff\u003C/sub> argument with everything else held constant.\u003C/p>\u003Cp>\u003Cstrong>Same-period cation series vs same-period anion series.\u003C/strong> When the metals on the left of a period (e.g., Na, Mg, Al) form their typical cations, they lose their entire valence shell, so Na⁺, Mg²⁺, Al³⁺ all share the [Ne] configuration of period 2. The nonmetals on the right of the same period (P, S, Cl) form anions by completing their valence shell, so P³−, S²−, Cl− all share the [Ar] configuration of period 3. The result: every typical anion of a period sits a full shell larger than every typical cation of the same period. P³−, S²−, Cl− are all larger than Na⁺, Mg²⁺, Al³⁺, even though their parent atoms come from the same row of the table.\u003C/p>",[41,77],106,[79],{"label":80,"body":81},"Try it: rank four ions that share ten electrons","\u003Cp>O²⁻, F⁻, Na⁺, and Mg²⁺ each hold exactly 10 electrons. Rank them from largest to smallest, then check below.\u003C/p>\u003Cp>\u003Cstrong>Answer:\u003C/strong> O²⁻ > F⁻ > Na⁺ > Mg²⁺. With identical electron clouds, the only variable left is nuclear charge: oxygen’s 8 protons hold the 10 electrons most loosely (biggest ion), while magnesium’s 12 protons grip the same 10 electrons hardest (smallest). In any isoelectronic series the rule collapses to one line: more protons, smaller ion. If your ranking disagreed, you likely compared parent atoms instead of counting protons against the shared electron total.\u003C/p>",{"heading":83,"content":84,"relatedObjectives":85},"Predicting Ionic vs Covalent Bonding from Periodic Trends","\u003Cp>The periodic trends collapse into two practical predictions for any pair of elements:\u003C/p>\u003Cp>\u003Cstrong>Bond type prediction (ionic vs covalent).\u003C/strong> Bond polarity is a continuum, not a set of bright lines: the polarity of a bond increases as the absolute value of the electronegativity difference between the two atoms increases. A bond between identical atoms (ΔEN = 0) is \u003Cstrong>nonpolar covalent\u003C/strong>; as ΔEN grows the bond becomes \u003Cstrong>polar covalent\u003C/strong> with the more electronegative atom carrying a partial negative charge (δ−) and the less electronegative atom carrying δ+; at very large ΔEN the electron pair is captured almost entirely by the more electronegative atom and the bond is described as \u003Cstrong>ionic\u003C/strong>. Common rule-of-thumb cutoffs (often ΔEN < ~0.4 nonpolar, ~0.4–1.7 polar covalent, > ~1.7 ionic) are useful pedagogical anchors but are not absolute thresholds — H–F at ΔEN ≈ 1.8 is typically presented as polar covalent rather than ionic, and many real bonds (AlCl\u003Csub>3\u003C/sub>, BeCl\u003Csub>2\u003C/sub>) sit on the borderline and show partial ionic character in some environments and partial covalent character in others.\u003C/p>\u003Cp>The qualitative shortcut covers most introductory cases: metal + nonmetal usually means ionic (most chlorides of group-1 and group-2 metals); nonmetal + nonmetal usually means covalent (CO\u003Csub>2\u003C/sub>, NH\u003Csub>3\u003C/sub>, CH\u003Csub>4\u003C/sub>); metal + metal means metallic bonding (treated as a separate category). Use ΔEN to sharpen the prediction at borderlines or to compare polarities between two covalent bonds (e.g., O–H is more polar than C–H because EN(O) > EN(C)).\u003C/p>\u003Cp>\u003Cstrong>Property prediction from valence-electron similarity.\u003C/strong> Elements in any one group (or column) have the same number of valence electrons. Same valence-electron count means similar chemistry: alkali metals (group 1) all form +1 cations and react vigorously with water; halogens (group 17) all form −1 anions; noble gases (group 18) are essentially inert. To \u003Cem>identify\u003C/em> an unknown element from its chemistry, find the group whose characteristic behavior matches and then place by period. To \u003Cem>predict\u003C/em> an element’s likely behavior, name its group and apply the family pattern.\u003C/p>\u003Cp>\u003Cstrong>Diagonal relationships.\u003C/strong> A second similarity pattern pairs elements that are not in the same group but lie one period down and one group to the right of each other — the most commonly cited examples are \u003Cstrong>Li and Mg\u003C/strong>, \u003Cstrong>Be and Al\u003C/strong>, and \u003Cstrong>B and Si\u003C/strong>. The two members of a diagonal pair tend to share similar charge-to-radius ratios and similar polarizing power, so their compounds and reactivity patterns track each other more closely than their column neighbors do. Treat diagonal relationships as a secondary similarity rule: same-group similarity is always your first move; diagonal similarity is a second-tier prediction to reach for when a problem points you at one of these specific pairs.\u003C/p>\u003Cp>Boundary note: this LO predicts \u003Cem>whether\u003C/em> a bond will be ionic or covalent from periodic position. The mechanism of ionic bonding (the actual electron transfer that converts neutral atoms into the cation and anion of an ionic compound) is taught and assessed under \u003Cstrong>T3 LO 3.7\u003C/strong> — see \u003Ca href=\"/learn/atomic-structure-and-isotopes\">T3: Atomic Structure and Isotopes\u003C/a>.\u003C/p>",[86],111,{"heading":88,"content":89,"relatedObjectives":90},"Trend Prediction: Quick-Check Strategy","\u003Cp>When you have to rank a mixed set of elements or predict which way a trend will tilt:\u003C/p>\u003Col>\u003Cli>\u003Cstrong>Locate every species on the periodic table\u003C/strong> (period, group, block).\u003C/li>\u003Cli>\u003Cstrong>Apply the trend arrow\u003C/strong>: down-and-left is bigger / lower IE / lower EN; up-and-right is smaller / higher IE / higher EN.\u003C/li>\u003Cli>\u003Cstrong>For ions, account for added or removed electrons\u003C/strong> first, then compare Z (more protons = smaller, when electron count matches).\u003C/li>\u003Cli>\u003Cstrong>Check for known exceptions\u003C/strong>: group 13 vs group 2, group 16 vs group 15 in IE; the Cr/Cu electron configurations from Topic 12.\u003C/li>\u003Cli>\u003Cstrong>Sanity-check with a neighbor\u003C/strong> — if your prediction puts F below Na in electronegativity, something went wrong.\u003C/li>\u003C/ol>\u003Cp>High-frequency errors: forgetting that ions can shift size by an entire shell (Na vs Na⁺); applying the trend across an exception without flagging it; treating ΔEN cutoffs as exact thresholds rather than guides.\u003C/p>",[41,77,68,42],{"title":92,"problem":93,"steps":94,"answer":100},"Ranking Isoelectronic Species by Radius","Arrange the following isoelectronic species in order of increasing ionic radius: N³⁻, O²⁻, F⁻, Na⁺, Mg²⁺. Justify the order using periodic-trend reasoning.",[95,96,97,98,99],"Confirm isoelectronic: each species has 10 electrons. N³⁻ (Z=7), O²⁻ (Z=8), F⁻ (Z=9), Na⁺ (Z=11), Mg²⁺ (Z=12).","All five species have the same electron configuration ([Ne] = 1s² 2s² 2p⁶), so the only variable that distinguishes them is nuclear charge Z.","Apply the rule: for isoelectronic species, more protons means stronger pull on the same 10 electrons, which means smaller radius.","Rank by Z (highest to lowest): Mg²⁺ (12) > Na⁺ (11) > F⁻ (9) > O²⁻ (8) > N³⁻ (7).","Reverse for increasing radius: Mg²⁺ \u003C Na⁺ \u003C F⁻ \u003C O²⁻ \u003C N³⁻.","Increasing radius: Mg²⁺ \u003C Na⁺ \u003C F⁻ \u003C O²⁻ \u003C N³⁻. With identical electron configurations, the species with the highest nuclear charge holds the 10 electrons closest, giving the smallest ionic radius.",[102,103,104],"OpenStax Chemistry 2e, Ch 6.4: Electronic Structure of Atoms (CC BY 4.0)","OpenStax Chemistry 2e, Ch 6.5: Periodic Variations in Element Properties (CC BY 4.0)","OpenStax Chemistry 2e, Ch 7.2: Covalent Bonding (CC BY 4.0)",[106,108,110,112,114,116,119,121,123,125,127,129,131],{"question":107},"What are valence electrons and how do you find them from a configuration?",{"question":109},"How do you read an element's group and period from the periodic table to predict its valence-electron count?",{"question":111},"What is effective nuclear charge (Z_eff) and how does it change across a period and down a group?",{"question":113},"How does atomic radius change across a period and down a group? Why?",{"question":115},"How does ionization energy change across a period and down a group? Why?",{"question":117,"hint":118},"What are the two well-known exceptions to the smooth IE trend across a period, and what causes them?","Look at Groups 2 vs 13, and Groups 15 vs 16.",{"question":120},"What is electronegativity and what trend does it follow?",{"question":122},"What is electron affinity and how does it differ from ionization energy?",{"question":124},"How does the size of a cation compare to its parent atom? What about an anion?",{"question":126},"What are isoelectronic species, and how do you rank them by ionic radius?",{"question":128},"How can you use electronegativity difference to predict whether a bond will be ionic or covalent?",{"question":130},"Why do elements in the same group typically show similar chemistry?",{"question":132,"hint":133},"What are diagonal relationships, and which element pairs are the standard examples?","Li/Mg, Be/Al, B/Si — a second-tier similarity pattern.",[135,136,137],"electron-structure-and-light","chemical-bonding-and-lewis-structures","atomic-structure-and-isotopes",[139,140,141,142,143,144,145],"Li","Na","K","F","Cl","O","Mg",[],[148,152],{"label":149,"equation":150,"note":151},"Effective Nuclear Charge (approximate)","Z_eff ≈ Z - (number of inner-shell electrons)","Useful as a quick estimator; Slater's rules give more accurate values",{"label":153,"equation":154,"note":155},"Bond-type rule of thumb (Pauling-scale guideline, not a strict cutoff)","ΔEN ≈ 0 → nonpolar covalent; intermediate ΔEN → polar covalent (more electronegative atom carries δ−); very large ΔEN → ionic","Polarity is treated as a continuum, not a set of strict thresholds. Common textbook bins are \u003C ~0.4 (nonpolar), ~0.4–1.7 (polar covalent), and > ~1.7 (ionic), but real bonds near or even above ΔEN = 1.7 (e.g., H–F at 1.8) typically sit within the polar-covalent series — the bins are anchors, not absolute thresholds.",{"title":157,"steps":158},"How to Predict the Bond Type Between Two Elements",[159,160,161,162,163,164],"Identify each element's group and period on the periodic table to anchor expected electronegativity.","Look up (or estimate from periodic position) the Pauling electronegativity of each element.","Calculate ΔEN = |EN_A - EN_B|.","Read polarity as a continuum: ΔEN ≈ 0 → nonpolar covalent; intermediate ΔEN → polar covalent (mark δ− on the more electronegative atom); very large ΔEN → ionic. Common textbook bins (\u003C ~0.4, ~0.4–1.7, > ~1.7) are useful anchors but are not absolute thresholds — H–F at ΔEN ≈ 1.8 is typically presented as polar covalent rather than ionic.","Sanity-check using element categories: metal + nonmetal usually means ionic; nonmetal + nonmetal usually means covalent.","Flag border cases (e.g., AlCl3, BeCl2) as polar covalent with significant ionic character rather than picking a single category.",{"question":166,"answer":167,"type":168},"Sulfur (Z = 16) and chlorine (Z = 17) are neighbors on the periodic table, yet removing the first electron from sulfur actually requires slightly less energy than removing the first electron from phosphorus (Z = 15), even though phosphorus has a lower atomic number. Why does phosphorus have a higher first ionization energy than sulfur?","Phosphorus has the electron configuration [Ne] 3s2 3p3, with a half-filled 3p sublevel. Half-filled sublevels have extra stability because all three p orbitals are singly occupied with parallel spins, maximizing exchange energy. Sulfur is [Ne] 3s2 3p4, which forces one 3p orbital to hold a paired electron. The electron-electron repulsion in that doubly occupied orbital makes it easier to remove one electron from sulfur, giving it a lower first ionization energy than phosphorus despite having a higher nuclear charge.","conceptual",[170,173],{"id":171,"problem":172,"type":168},"pt-13-1","Arrange the following in order of increasing atomic radius: Na, Mg, K, Ca. Explain your reasoning using periodic trends.",{"id":174,"problem":175,"type":168},"pt-13-2","For each pair, predict whether the bond formed is ionic, polar covalent, or nonpolar covalent: (a) Na and Cl, (b) C and O, (c) H and H, (d) K and F.",{"workedExampleCount":177,"hasWorksheets":178},12,true,[180,181,182,183,184,185,186],"periodic trends","atomic radius","ionization energy","electronegativity","electron affinity","isoelectronic species","ionic vs covalent bonding","2026-07-16",6,{"id":177,"slug":135,"lesson":177,"title":190,"shortTitle":191,"description":192,"category":9,"objectiveCount":193,"problemCount":194},"Electron Structure and Light","Electron Structure","Build the modern model of the atom: shells and orbitals, quantum numbers, electron configurations, orbital diagrams, common exceptions, and the connection to light through the Bohr model and de Broglie wavelength.",9,43,{"id":196,"slug":136,"lesson":196,"title":197,"shortTitle":198,"description":199,"category":200,"objectiveCount":201,"problemCount":202},14,"Chemical Bonding and Lewis Structures","Lewis Structures","Draw Lewis structures for molecules and polyatomic ions that satisfy the regular octet (and the duet for hydrogen), apply the octet rule and identify its exceptions, calculate formal charges, and identify resonance structures.","bonding-structure",4,22,1785108608108]