The correct order of electron gain enthalpy (most negative to least negative) for halogens is:

Electron gain enthalpy (ΔegH, also called electron affinity when expressed as the negative of the energy change) is defined as the enthalpy change accompanying the addition of one electron to a neutral gaseous atom in its ground state to form a gaseous anion: X(g) + e- → X-(g), ΔegH. The sign convention used in modern IUPAC recommendations: negative value (exothermic) means energy is released when the electron is added — the anion is more stable than the neutral atom + free electron system, and the atom has a positive "electron affinity" in the traditional sense. Measurement: electron gain enthalpies cannot be measured directly by calorimetry (gas-phase atomic processes are not easily performed calorimetrically). They are determined indirectly using the Born-Haber cycle for ionic compounds: by measuring the lattice energy, enthalpy of formation, ionisation energy, enthalpy of atomisation, and enthalpy of dissociation of the halogen, the electron affinity of the halogen can be calculated as the only unknown in the cycle. Modern high-precision measurements use photoelectron spectroscopy techniques that directly measure the energy needed to remove an electron from a gaseous anion (the detachment energy = electron affinity). Values for the halogens: F = -328 kJ/mol, Cl = -349 kJ/mol, Br = -325 kJ/mol, I = -295 kJ/mol, At = -270 kJ/mol (estimated). The anomalous lower electron affinity of F compared to Cl is one of the most important periodicity anomalies in the periodic table.

Fluorine, the first member of Group 17, is arguably the most anomalous element in the periodic table, deviating from the trends shown by the heavier halogens in more ways than any other first-period element deviates from its group. These anomalies arise from its extremely small size, the absence of d-orbitals in the valence shell (period 2), and its extraordinarily high electronegativity and oxidising power. Size: F is the smallest halogen (covalent radius 64 pm vs Cl 99 pm, Br 114 pm, I 133 pm). The small size leads to: high charge density, strong electrostatic interactions, high lattice energies of fluorides. Bond strength: the F-F bond in F2 is anomalously WEAK (bond dissociation energy F-F = 155 kJ/mol vs Cl-Cl = 242 kJ/mol vs Br-Br = 193 kJ/mol). This is because the two F atoms in F2 are so small that the lone pairs on each F are very close together, causing strong lone pair-lone pair repulsion that weakens the F-F bond. Despite this weak F-F bond, F2 is the most powerful oxidising agent among the halogens — partly because of the weak F-F bond (easy to break the oxidant), partly because of the strong H-F, C-F, and other X-F bonds that form (the thermodynamic driving force). Oxidation state: F can only be -1 or 0 (never positive) because it has no d-orbitals available and is the most electronegative element. Other halogens (Cl, Br, I) can have positive oxidation states (+1, +3, +5, +7) when bonded to more electronegative atoms (F or O), using d-orbitals for expansion of the valence shell.

Ionisation enthalpy (or ionisation energy, IE) is the minimum energy required to remove an electron from a neutral gaseous atom in its ground state to form a gaseous cation: X(g) → X+(g) + e-. Unlike electron gain enthalpy (always endothermic for removal), ionisation enthalpy is always positive (energy must be supplied to overcome the attraction between the electron and the nucleus). Trends in IE: Across a period (left to right): IE generally increases because nuclear charge increases while electrons are added to the same shell (same n, similar shielding). More positive nucleus → stronger attraction → higher IE. Exceptions: IE(Be) > IE(B) because B has one electron in 2p (easier to remove from higher-energy 2p than from completely filled 2s). IE(N) > IE(O) because N has a half-filled 2p3 (extra stability of half-filled subshell) while O must pair an electron in 2p (increased electron-electron repulsion in paired orbital makes it easier to remove). Down a group: IE decreases because atomic radius increases (valence electrons farther from nucleus) and inner electron shielding increases (more inner shells between nucleus and valence electrons) → net effective nuclear charge on valence electrons decreases → lower energy required to remove an electron. Successive ionisation energies: IE1 < IE2 < IE3 < ... (each subsequent electron is removed from a smaller, more positively charged ion). Large jump in successive IE when an electron must be removed from a completely filled inner shell (e.g., Na: IE1 = 496, IE2 = 4562 kJ/mol — the huge jump at IE2 reflects removal from the filled n=2 shell).

Electronegativity, first systematically quantified by Linus Pauling in 1932, is the tendency of an atom in a covalent bond to attract the shared electron pair toward itself. It is a property of bonded atoms in a particular molecular context, not of isolated atoms (unlike ionisation energy or electron affinity). Multiple scales: Pauling scale (dimensionless, based on bond dissociation energies, F=4.0 as reference): most commonly used. Mulliken scale (based on average of IE and EA): EN_M = (IE + EA)/2. Allred-Rochow scale (based on electrostatic force on electron): EN_AR = (0.744 + 0.359Z_eff)/r^2. All scales give essentially the same relative ordering. Trends: Across a period: electronegativity increases (higher Z, smaller radius → stronger nuclear attraction for bonding electrons). Down a group: decreases (larger radius → bonding electrons farther from nucleus, less strongly attracted). Most electronegative: F(4.0), O(3.5), N and Cl(3.0), Br(2.8). Least electronegative (most electropositive): Cs(0.7), Fr(0.7), Ba(0.89), Ra(0.89). Carbon EN = 2.5. Chemical significance: electronegativity differences determine bond polarity. If |EN_A - EN_B| = 0: nonpolar covalent. 0 < difference < ~1.5: polar covalent. >1.7: predominantly ionic. Electronegativity determines the direction of bond dipoles, molecular polarity, acidity of O-H bonds (more electronegative element attached to OH → more acidic), basicity of N lone pairs (more electronegative substituents → less basic), and the inductive effect in organic chemistry.

Atomic radius is one of the most fundamental periodic properties and its trends underlie the trends in virtually all other periodic properties. Several different definitions: Covalent radius: half the internuclear distance between two atoms of the same element in a covalent bond (e.g., Cl-Cl in Cl2: bond length 198 pm → r_cov = 99 pm). Van der Waals radius: half the distance between adjacent atoms in non-bonded contact (always > covalent radius; reflects size of the electron cloud). Metallic radius: half the distance between adjacent metal atoms in the metal crystal lattice. Ionic radius: the effective size of an ion in a crystal lattice (determined from X-ray crystallography). Trends: Across a period: atomic radius decreases from left to right because nuclear charge (Z) increases while electrons are added to the same principal shell (n) with similar shielding. The effective nuclear charge Z_eff = Z - σ (where σ = shielding constant) increases across the period, causing the electron cloud to contract. Anomaly: noble gas atoms have larger atomic radii than adjacent halogens because van der Waals radii of noble gases are compared with covalent radii of halogens — not a fair comparison. Down a group: atomic radius increases because each successive element adds a new electron shell (higher n), and the valence electrons are in a shell farther from the nucleus. Lanthanide contraction (discussed earlier) makes the 5d metals nearly the same size as the 4d metals, and similarly for post-lanthanide 6p elements vs post-5d 5p elements.

The periodic trends in atomic properties — ionisation energy, electron affinity, atomic radius, electronegativity, and others — collectively determine the chemical reactivity and reaction chemistry of elements. Reactivity of metals: metals react by losing electrons (oxidation). Higher reactivity = lower IE, lower oxidising potential = more electropositive. Most reactive metals: alkali metals (Li, Na, K, Rb, Cs) and alkaline earth metals (Ca, Sr, Ba). The activity series (electrochemical series) ranks metals in order of decreasing reducing power (decreasing tendency to lose electrons, decreasing reactivity): Li, K, Ba, Ca, Na, Mg, Al, Zn, Fe, Ni, Sn, Pb, H, Cu, Ag, Au. Metals above H reduce H+ (displace H2 from acid); metals above Cu can reduce water; the most reactive (K, Na, Ca) react vigorously with cold water. Reactivity of non-metals: non-metals react by gaining electrons (reduction). Higher reactivity = higher electron affinity, higher electronegativity, lower atomic radius. Most reactive non-metals: F > O > Cl > Br > I > S > N. F2 reacts with everything including noble gases (XeF2, XeF4), glass (SiO2 + 4HF → SiF4 + 2H2O), and even platinum. O2 reacts with most metals and non-metals (combustion). Cl2 reacts with most metals and non-metals under suitable conditions. Noble gas reactivity: only Xe and Kr form stable compounds under normal conditions (XeF2, XeF4, XeF6, XeO3, XeOF4, KrF2). He, Ne, Ar, Rn do not form stable chemical compounds under normal conditions.