Isotopes, Atomic Masses, Electronic Structure, and Periodicity

Isotopes and Atomic Masses

• Definition of Isotopes: Different atoms of the same element that have the same number of protons but different numbers of neutrons.
  • Example: Hydrogen atoms exist in three forms:
    • Hydrogen-1 (Protium): 1 proton, 0 neutrons, mass number 1.
    • Hydrogen-2 (Deuterium): 1 proton, 1 neutron, mass number 2.
    • Hydrogen-3 (Tritium): 1 proton, 2 neutrons, mass number 3.
• Properties of Isotopes:
  • Chemical Properties: Same, due to the same number of electrons.
  • Physical Properties: Exhibit slight differences (e.g., density and mass) due to differences in neutron number and isotopic masses.
• Element Composition: Most elements exist as a mixture of isotopes with varying ratios.
  • Example: Normal carbon sample contains 98.99\% carbon-12 and 1.1\% carbon-13.
• Atomic Mass: An average mass value calculated for a sample element, as a sample contains many atoms of various isotopes.
  • Measurement Difficulty: Atoms are too tiny and their mass is very small (ranging from 1.66 \times 10^{-24} \text{ g} to 3.95 \times 10^{-22} \text{ g}).
  • Standard Atom: Carbon-12 is used as a standard for comparison.
• Relative Atomic Mass (A_r): Defined as the average mass of an atom relative to one-twelfth the mass of an atom of the isotope carbon-12.
  • Formula: A_r = \frac{\text{average mass of an atom of an element}}{\frac{1}{12} \times \text{mass of one atom of carbon-12}}
  • Unit: Has no unit because it is a ratio of two measurements of the same unit.
• Relative Isotopic Mass: The mass of an atom of a particular isotope relative to one-twelfth the mass of an atom of the isotope carbon-12.
  • Example: Chlorine-35 (^{35}\text{Cl}) has a relative isotopic mass of 35. The relative atomic mass of chlorine is 35.5 due to the average of naturally occurring isotopes.
• Calculation of Relative Atomic Mass: Multiply each isotopic mass by its relative abundance, add the values, and divide by 100.
  • Formula: A_r = \Sigma \frac{(\text{relative isotopic mass} \times \text{abundance of isotope})}{100}
  • Example for Chlorine: Chlorine-35 (75\%) and Chlorine-37 (25\%)
    • A_r = \frac{(35 \times 75) + (37 \times 25)}{100} = 35.5
• Unified Atomic Mass Unit (u): The standard unit for measuring relative atomic mass, defined as one-twelfth the mass of a carbon-12 atom.
  • 1 \text{ u} = 1.66 \times 10^{-27} \text{ kg}
  • Example: The atomic mass of chlorine is 35.5 \text{ u}.
• Terminology Note: "Relative atomic mass" (A_r) is used in the British system, while "average atomic mass" is used in the American system.
• Dalton's Atomic Theory and Isotopes: Dalton's proposal that atoms of a given element are identical was disproved by the discovery of isotopes.

Mass Spectrometer

• Purpose: An extremely sensitive device used to measure the masses of different isotopes and their relative abundances in a given sample.
• Simplified Diagram Components: Heater element, ionization chamber (electron beam), electric field (acceleration), electromagnet (deflection), detector.
• Working Mechanism:
  1. Vaporization: Elemental sample is vaporized by a heating device.
  2. Ionization: Vaporized atoms are bombarded by fast-moving electrons, knocking off electrons and creating mostly +1 charged ions.
  3. Acceleration: Ions are accelerated in an electrical field.
  4. Deflection: Ions pass into a magnetic field, where they are deflected by varying degrees according to their masses (lighter ions deflect more).
  5. Detection: Deflected ions hit a detector plate at different positions.
  6. Spectrum Production: The spectrometer analyzes these positions to produce a mass spectrum.
• Mass Spectrum: A graph that records the relative masses of isotopes versus their relative abundance in the sample.
  • Y-axis: Relative abundance (\%) of isotopes.
  • X-axis: Mass-to-charge ratio (\text{m/e}).
  • Interpretation: For single positively charged ions, the mass-to-charge ratio effectively represents the mass of the ion.
  • Average Mass Calculation: Add the products of each isotopic mass and its relative abundance.
    • Average mass = \sum (\text{isotopic mass} \times \text{relative abundance})
  • Example: Zirconium (Zr) spectrum shows five isotopes:
    • Isotopic mass 90: 51.5\% abundance
    • Isotopic mass 91: 11.2\% abundance
    • Isotopic mass 92: 17.1\% abundance
    • Isotopic mass 94: 17.4\% abundance
    • Isotopic mass 96: 2.8\% abundance
    • A_r = \frac{(51.5 \times 90) + (11.2 \times 91) + (17.1 \times 92) + (17.4 \times 94) + (2.8 \times 96)}{100} = 91.3
  • Example: Lead (Pb) spectrum (Z=82) shows four peaks/isotopes:
    • 204Pb: 1.4\% (122 neutrons)
    • 206Pb: 24.1\% (124 neutrons)
    • 207Pb: 22.1\% (125 neutrons)
    • 208Pb: 52.4\% (126 neutrons)
    • Average atomic mass = \frac{(204 \times 1.4) + (206 \times 24.1) + (207 \times 22.1) + (208 \times 52.4)}{100} = 207.2
• Advanced Uses: Mass spectrometers can also determine structures of organic molecules, though not discussed in this chapter.

Electronic Structure

Nature of Light

• Historical View (pre-17th century): Light consisted of streams of particles.
• Wave Nature Emergence (1665): A new perspective suggested light has a wave nature.
• James Maxwell (1865): Established the foundations, describing light as electromagnetic waves.
• Electromagnetic Radiation: A form of radiant energy with wavelike characteristics that travels in a vacuum at the speed of light.
  • Speed of Light (c): 3.00 \times 10^8 \text{ m s}^{-1}.
  • Classification: Based on wavelength, frequency, and speed.
• Wavelength (\lambda): The distance between two consecutive peaks or troughs in a wave.
• Frequency (\nu): The number of waves (cycles) per second that pass a given point in space.
• Relationship: Wavelength and frequency are inversely proportional.
  • Formula: c = \lambda \nu
    • c: speed of light (3.00 \times 10^8 \text{ m} \cdot \text{s}^{-1})
    • \lambda: wavelength (meters, m)
    • \nu: frequency (hertz, Hz)
• Electromagnetic Spectrum: Categorizes various types of electromagnetic radiation.
  • Examples: Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
  • Trends: Increasing wavelength corresponds to decreasing frequency and vice versa.

Quantized Energy

• Matter Emitting EM Radiation: Solids glow when heated, changing color with energy applied (e.g., electric stove coil from red to yellow).
  • The intensity and wavelength of emitted radiation depend on the absorbed energy.
• Max Planck (1900): Proposed that energy is quantized, transferred only in multiples of discrete "packets" of minimum size, called quanta.
  • Energy of a Quantum (Photon): E = h\nu
    • E: energy absorbed or released (Joules, J)
    • h: Planck's constant (6.626 \times 10^{-34} \text{ J} \cdot \text{s})
    • \nu: radiation frequency (hertz, Hz)
  • Higher energy absorbed means higher frequency and shorter wavelength of emitted radiation, explaining color changes.
• Albert Einstein (1905): Suggested light has a dual nature: corpuscular (stream of particles called photons or quanta) and wavelike, based on Planck's findings.
  • Photon energies are quantized; only specific amounts of energy are possible.

Photoelectric Effect

• Definition: The phenomenon observed when the surface of a metal emits electrons when exposed to light of a minimum frequency.
• Threshold Frequency: The minimum frequency required for photons to strike the metal and allow electrons to overcome attractive forces holding them in the metal.
  • Each type of metal has a specific threshold frequency.
• Electron Emission: Electrons are emitted only if photons have sufficient energy (frequency greater than threshold frequency).
• Intensity Relationship: The number of emitted electrons increases with the intensity of light.
• Significance: Could not be explained by the wavelike nature of light alone, supported Einstein's particle theory of light.

Electronic Structure of the Atom and Energy Levels

• Bohr Model: Assigned specific energy amounts to electrons but had limitations regarding electron interactions.
• Currently Accepted Atomic Model: Describes electrons occupying specific energy levels (electron shells).
• Energy Level / Electron Shell: Refers to a state of energy of the electron, not its specific location.
  • Principal Quantum Number (n): A positive integer assigned to each energy level, indicating:
    • Average distance of the electron from the nucleus.
    • Energy possessed by that electron.
• Energy and Distance: Electron energy increases as it moves away from the nucleus.
  • n=1 is the lowest energy level, closest to the nucleus.
• Quantized Energy Levels: Energy levels have fixed (discrete) values; an electron's energy cannot have an intermediate value.
• Ground State: The lowest energy level an electron can possess (e.g., n=1 for a hydrogen atom).
• Excited State: If enough energy is transferred, an electron moves to a higher energy level (n > 1).
• Photon Emission: When an excited electron returns to its ground state, it releases the absorbed energy by emitting a photon with a specific wavelength.
  • Energy Change Formula: \Delta E = h\nu = \frac{hc}{\lambda}

Atomic Spectrum of Hydrogen

• Proof of Quantized Energy Levels: Obtained by analyzing light emitted by excited hydrogen atoms.
• Experimental Setup: Hydrogen molecules (\text{H}_2) in a bulb, high electric voltage breaks bonds, excites electrons.
• Light Emission: Excited electrons release energy as visible light of various wavelengths, producing the hydrogen emission spectrum.
• Continuous Spectrum: Produced by white light passed through a prism, showing a rainbow-like spectrum with all wavelengths of visible light.
• Line Spectrum: Produced by light from an excited hydrogen bulb passed through a prism, showing only a few discrete wavelengths.
  • Significance: Indicates that only certain energies are allowed for the electron of an excited hydrogen atom, proving electron energy levels are quantized.
• Calculating Energy Change: Distinct wavelengths from the hydrogen spectrum can be used in Planck's equation to determine \Delta E between energy levels.
  • Solved Example (n=1 to n=2 excitation): Given \Delta E = 1.633 \times 10^{-18} \text{ J}
    • 1.633 \times 10^{-18} \text{ J} = \frac{(6.63 \times 10^{-34} \text{ J} \cdot \text{s}) \times (3.00 \times 10^8 \text{ m} \cdot \text{s}^{-1})}{\lambda}
    • \lambda = 1.22 \times 10^{-7} \text{ m}

Electron Capacity of Energy Levels

• Maximum Number of Electrons: Given by the expression 2n^2, where n is the principal quantum number.
  • Level n=1: 2(1)^2 = 2 electrons.
  • Level n=2: 2(2)^2 = 8 electrons.
  • Level n=3: 2(3)^2 = 18 electrons.
  • Level n=4: 2(4)^2 = 32 electrons.

Subshells and Atomic Orbitals

• Subshells (Sublevels): Each energy level consists of one or more subshells, designated by letters (s, p, d, f).




• Atomic Orbital: A specific three-dimensional region around the nucleus indicating a probable location of an electron, accommodating a maximum of two electrons.




• Characteristics of Subshells:

• s subshell:
  • Consists of one spherical orbital.
  • Exists in all energy levels (n \geq 1).
  • Maximum of 2 electrons.
  • Represented as a square with two opposite arrows (\uparrow\downarrow).
• p subshell:
  • Consists of three dumbbell-shaped orbitals (\text{p}x, \text{p}y, \text{p}_z).
  • Exists in energy levels with n \geq 2.
  • Maximum of 6 electrons (two in each orbital).
• d subshell:
  • Consists of five orbitals (four have a four-leaf clover shape, one is two lobes with a toroid).
  • Exists in energy levels with n \geq 3.
  • Maximum of 10 electrons.
• f subshell:
  • Consists of seven orbitals (complex shapes, omitted for this course).
  • Exists in energy levels with n \geq 4.
  • Maximum of 14 electrons.

• n=1: 1^2 = 1 orbital (1s orbital).
• n=2: 2^2 = 4 orbitals (one s, three p).

Electron Configuration

• Definition: The specific arrangement of electrons around an atom's nucleus.
• Three Basic Rules:
  1. Aufbau principle
  2. Pauli exclusion principle
  3. Hund's rule

Aufbau Principle

• Statement: Electrons in atoms tend to occupy the lowest possible energy arrangement, filling the lowest energy orbital first.
• Energy Order:
  • An s orbital of an energy level is lower in energy than the s orbital of the next higher energy level (e.g., 2s < 3s).
  • Within a specific energy level, the energy order is s < p < d < f.
  • Degenerate Orbitals: Orbitals within the same subshell have the same energy (e.g., all five 4d orbitals are degenerate).
• Energy Overlap: Starting at the third energy level, subshell energies can overlap (e.g., 3d is higher in energy than 4s).
• Order of Filling: 1 ext{s}2 ext{s}2 ext{p}3 ext{s}3 ext{p}4 ext{s}3 ext{d}4 ext{p}5 ext{s}4 ext{d}5 ext{p}6 ext{s}4 ext{f}5 ext{d}6 ext{p}7 ext{s}5 ext{f}6 ext{d}7 ext{p}
  • This sequence can be visualized using Aufbau diagrams.
  • Sequence for filling up to 88 electrons: 1 ext{s}^22 ext{s}^22 ext{p}^63 ext{s}^23 ext{p}^64 ext{s}^23 ext{d}^{10}4 ext{p}^65 ext{s}^24 ext{d}^{10}5 ext{p}^66 ext{s}^24 ext{f}^{14}5 ext{d}^{10}6 ext{p}^67 ext{s}^2

Pauli Exclusion Principle

• Statement: Each atomic orbital can be occupied by a maximum of two electrons, which must have opposite spins (one clockwise, one counterclockwise).
  • Represented by two vertical arrows pointing in opposite directions (\uparrow\downarrow).

Hund's Rule

• Statement: Orbitals of equal energy (degenerate orbitals) are first occupied by the maximum number of unpaired electrons having the same spin, to minimize electron-electron repulsions. After all degenerate orbitals are singly filled, remaining electrons can start pairing with opposite spins.
  • Example for p subshell with four electrons:
    1. Three electrons with the same spin fill the ext{p}x, \text{p}y, \text{p}_z orbitals (\uparrow \uparrow \uparrow).
    2. The fourth electron pairs with one of the existing electrons, with an opposite spin (e.g., \uparrow\downarrow \uparrow \uparrow).

Determining Electron Configuration

• Atomic Number: Used to determine the number of electrons for a neutral atom.
• Example: Carbon (Z=6): Six protons, six electrons.
  • 1s^2 (two electrons in 1s)
  • 2s^2 (two electrons in 2s)
  • 2p^2 (two electrons, one in each of two 2p orbitals, with same spin) - Orbital diagram: \underset{1s}{\uparrow\downarrow} \underset{2s}{\uparrow\downarrow} \underset{2p}{\uparrow \uparrow _}
• Free Radicals: Atoms with one or more unpaired electrons in their orbitals.
  • Example: Fluorine (F): 1s^22s^22p^5 - Has one unpaired electron in its 2p subshell.

Exceptions to Aufbau Principle

• Occur for elements with atomic number greater than 23 (e.g., Chromium ({24}\text{Cr}) and Copper ({29}\text{Cu})).
• Reason: Half-filled and fully filled subshells are more stable than partially filled subshells.
  • Chromium (Cr): Predicted: [Ar]4s^23d^4; Correct: [Ar]4s^13d^5 (half-filled 4s and half-filled 3d).
  • Copper (Cu): Predicted: [Ar]4s^23d^9; Correct: [Ar]4s^13d^{10} (half-filled 4s and fully filled 3d).

Valence Electrons and Noble Gas Configuration

• Valence Electrons: Electrons in the outermost occupied energy level (valence shell) of an atom.
• Noble Gases (He, Ne, Ar, Kr, Xe, Rn): Have full valence shells, making them particularly stable and unreactive.
• Noble Gas Configuration: Atoms tend to gain, lose, or share electrons to achieve a full valence shell, mimicking noble gas configurations.
  • Example: Hydrogen: Gains or shares electrons to attain helium's configuration.

Electron Configuration Notations

• Full Electron Configuration (1s² notation): Lists all occupied subshells with electron counts.
• Box Notation / Orbital Diagram: Uses boxes (or lines) for orbitals and arrows for electrons.
• Shorthand Electron Configuration (Noble Gas Notation): Uses the symbol of the noble gas from the preceding period in brackets, followed by the configuration of the remaining orbitals.
  • Example: Potassium (_{19}\text{K}): Full: 1s^22s^22p^63s^23p^64s^1; Shorthand: [Ar]4s^1
    • [Ar] represents 1s^22s^22p^63s^23p^6
  • Solved Example: Germanium (Z=32):
    • Full: 1s^22s^22p^63s^23p^64s^23d^{10}4p^2
    • Noble Gas: [Ar]3d^{10}4s^24p^2 (note: 3d listed before 4s in noble gas notation but fills after 4s)

Electron Configurations for Ions

• General Rule: Same rules as for neutral atoms, aiming to attain a noble gas configuration.
• Positive Ions (Cations): Formed by removing electrons, usually from the outermost subshells.
  • Procedure: Subtract the cation's charge from the atomic number to get electron count. Remove electrons from the highest principal quantum number subshell first.
  • Example: Calcium (_{20}\text{Ca}) to Ca^{2+}:
    • Ca: 1s^22s^22p^63s^23p^64s^2
    • Ca^{2+}: 20-2=18 electrons; remove 2 electrons from 4s (outermost).
    • Ca^{2+}: 1s^22s^22p^63s^23p^6 (same as Argon).
  • Transition Metals Exception: For elements ending with a d subshell, electrons are removed from the s subshell with the highest principal quantum number first, even if it filled before the d subshell.
    • Example: Iron (_{26}\text{Fe}) to Fe^{2+} and Fe^{3+}:
      • Fe: 1s^22s^22p^63s^23p^64s^23d^6
      • Fe^{2+}: Remove 2 electrons from 4s. 1s^22s^22p^63s^23p^63d^6 or [Ar]3d^6
      • Fe^{3+}: Remove 2 electrons from 4s and 1 from 3d. 1s^22s^22p^63s^23p^63d^5 or [Ar]3d^5
  • Solved Example: Cu^{2+} (Z=29):
    • Cu (exception): 1s^22s^22p^63s^23p^64s^13d^{10}
    • Cu^{2+}: Remove 1 from 4s and 1 from 3d. 1s^22s^22p^63s^23p^63d^9
• Negative Ions (Anions): Formed by gaining electrons. Electrons are added to the outermost subshell.
  • Procedure: Add the anion's charge to the atomic number to get electron count. Add electrons to the outermost subshell.
  • Example: Fluorine (_{9}\text{F}) to F^-:
    • F: 1s^22s^22p^5
    • F^-: 9+1=10 electrons; add to 2p.
    • F^-: 1s^22s^22p^6 (same as Neon).

Coulomb's Law and Photoelectron Spectroscopy (PES)

Binding Energy and Kinetic Energy of Electrons

• Binding Energy: Minimum energy required to overcome attractive forces between an electron and the nucleus in an atom and release the electron.
• Kinetic Energy: Energy of motion of the ejected electron. Greater kinetic energy means greater electron speed.
• Energy Conservation: Energy of the photon = binding energy + kinetic energy.
  • Photon energy is transformed into binding energy (to remove the electron) and kinetic energy (to eject it).
• Distance and Energy:
  • Further electron from nucleus = less attraction, smaller binding energy, greater kinetic energy, faster speed.
  • Example: Electron at n=2 has more binding energy than n=4. For the same photon energy, an electron from n=2 will have less kinetic energy than one from n=4.

Coulomb's Law

• Describes: Electrical force (F) and energy (E) between two charged particles (Q1, Q2) separated by a distance (r).
  • Force Formula: F = k\frac{Q1 Q2}{r^2}
  • Energy Formula: E = k\frac{Q1 Q2}{r}
    • This also means E = F \times r
• Implications for Electron Binding Energy:
  • Distance (r): Closer electron to nucleus (smaller r) = stronger binding energy (more energy needed to remove).
  • Nuclear Charge (Q): Greater nuclear charge (Q) = stronger binding energy (more energy needed to remove).

Photoelectron Spectroscopy (PES)

• Technique: Used to determine the binding energy of electrons emitted by an element exposed to light of a specific frequency.
• Process: Measures the kinetic energy of the ejected electron and compares it to the photon's energy to deduce the electron's binding energy.
• Data Application: Provides a method to deduce the shell structure of an atom by measuring electron energies in each subshell.
• PES Spectrum Analysis:
  • Peak Position (X-axis, Binding Energy): Related to the energy required to remove an electron from a subshell.
    • Higher binding energy corresponds to subshells closer to the nucleus.
  • Peak Intensity (Y-axis, Relative Number of Electrons): A measure of the number of electrons in that particular subshell.
• Example: PES Spectrum of an Unknown Element (Neon)
  • Peak 1: Highest binding energy, indicates 1s subshell. Height indicates 2 electrons (1s^2).
  • Peak 2: Lower binding energy than Peak 1, indicates 2s subshell. Height indicates 2 electrons (2s^2).
  • Peak 3: Even lower binding energy than Peak 2, indicates 2p subshell. Height is three times Peaks 1 & 2, indicates 6 electrons (2p^6).
  • Conclusion: Electronic configuration is 1s^22s^22p^6. The element is Neon.

Structure of the Periodic Table

• Organization Principles: Organized by increasing atomic number and reflects elements' electronic structure.
• Columns (Groups): 18 vertical columns.
• Rows (Periods): 7 horizontal rows.

Periods in the Periodic Table

• Correspondence: Each row corresponds to an energy level (n).
• Electron Filling: Elements in a period have their outer (valence) electrons in the same energy level.
  • Period 1: Electrons fill n=1 (Hydrogen, Helium). Total 2 elements (2n^2 = 2(1)^2 = 2).
  • Period 2: Electrons fill n=2 (Lithium to Neon). Total 8 elements (2n^2 = 2(2)^2 = 8).
  • Chemical Behavior: Elements in the same period can have drastically different chemical behavior.

Chemical Groups / Families

• Labeling:

• IUPAC System: Groups numbered 1 to 18.
• North American System: Arabic or Roman numerals followed by 'A' (e.g., 1 ext{A}, 2 ext{A}, 13=3 ext{A}, \text{etc.}).

• They tend to react similarly to acquire a full valence shell (noble gas configuration).

• Group 1 (1A): Alkali metals (e.g., Sodium, Potassium – [Ne]3s^1, [Ar]4s^1 respectively).
• Group 2 (2A): Alkaline earth metals
• Group 17 (7A): Halogens
• Group 18 (8A): Noble gases (e.g., Helium, Neon, Argon, Krypton, Xenon, Radon).

• Categorization: Based on the subshell in which the valence electrons reside.
  • s-block: Groups 1 and 2 (valence electrons in an s subshell).
  • p-block: Groups 13 through 18 (valence electrons in both s and p subshells).
  • d-block: Groups 3 through 12 (transition metals).
  • f-block: Lanthanides (4f subshells) and Actinides (5f subshells) - usually separated below the main table.

Atomic and Ionic Radii

Atomic Radius

• Definition: An estimate of the distance between the nucleus of an atom and its outermost electron.
• Measurement: Determined by measuring the distance between the nuclei of two identical bonded atoms and dividing by two.
• Trends Down a Group (Top to Bottom):
  • Increases.
  • Explanation: As n (principal quantum number) increases, valence electrons are in higher energy levels, farther from the nucleus. While nuclear charge increases, the dominant effect is the shielding effect from inner-shell electrons, weakening the attraction between the nucleus and outermost electrons.
  • Example: Chlorine (Period 3) has a larger radius than Fluorine (Period 2) because its outermost electron is in n=3 vs. n=2 for fluorine, and it experiences greater shielding.
• Trends Across a Period (Left to Right):
  • Decreases.
  • Explanation: The number of protons (nuclear charge) increases, pulling valence electrons more closely to the nucleus. The number of core electrons remains the same, so the shielding effect does not change significantly. Electrons are added to the same valence shell.
  • Example: Sodium (Z=11) has a larger radius than Chlorine (Z=17) because chlorine has a greater nuclear charge pulling electrons more strongly, with similar shielding.
• Overall Trends:
  • Largest elements: Toward the left and bottom of the periodic table.
  • Smallest elements: Toward the right and top of the periodic table.
  • Helium is the smallest element.
  • Alkali metals (Group 1) are the largest elements in their respective rows.
  • Noble gases (Group 18) are the smallest elements in their respective rows.

Ionic Radius

• Difference from Atomic Radius: Trends for ions differ significantly from neutral atoms.
• Cations (Positive Ions):
  • Smaller than their neutral atoms.
  • Explanation: When an atom loses valence electrons, its outermost energy level often changes (e.g., K to K^+ loses 4s^1 and has Ar configuration). The remaining electrons are drawn closer to the nucleus by the positive nuclear charge.
  • Example: K (197 \text{ pm}) is much larger than K^+ (133 \text{ pm}).
• Anions (Negative Ions):
  • Larger than their neutral atoms.
  • Explanation: When an atom gains an electron, the new electron increases repulsion among existing valence electrons. This increased repulsion forces electrons away from one another, expanding the overall size of the anion.
  • Example: Cl (99 \text{ pm}) is smaller than Cl^- (181 \text{ pm}).
• Trends Across a Period (Left to Right) for Ions:
  • Ionic radii decrease.
  • Explanation: Nuclear charge increases, pulling valence electrons closer. However, anions are generally much larger than cations because anions typically have one more energy level occupied by valence electrons, making them farther from the nucleus.
• Isoelectronic Ions: Ions containing the same number of electrons (e.g., K^+, Ca^{2+}, Cl^-, S^{2-} all have 18 electrons).
  • Trend: Ionic radius decreases as nuclear charge increases.
  • Explanation: A higher number of protons in the nucleus leads to stronger attraction between the nucleus and the same number of electrons, resulting in a smaller ion.

Ionization Energy

• Definition: The energy required to remove an electron from each gaseous atom or ion in a mole of atoms or ions.
  • Process: Always endothermic (requires energy).
  • Magnitude: More strongly attracted electrons require more energy (higher IE).
  • Unit: Kilojoules per mole (kJ ext{mol}^{-1}).
  • Binding Energy: At this level, the ionization energy to remove a specific electron is considered its binding energy.
• First Ionization Energy (IE_1): Energy required to remove one electron from each atom of a mole of gaseous neutral atoms to form one mole of gaseous +1 ions.
  • Generic Reaction: X(g) + IE_1 \rightarrow X^+(g) + e^-
• Factors Influencing Ionization Energy:
  1. Atomic Size: Smaller atoms (electrons closer to nucleus) tend to retain electrons more effectively, thus having higher IE.
  2. Shielding Effect: Core electrons repel valence electrons, shielding them from nuclear attraction. Increased shielding (more energy levels) decreases IE.
  3. Nuclear Charge: Increased nuclear charge across a period increases attraction, requiring more energy to remove an electron, thus increasing IE.
• General Trends:
  • Increases across a period (left to right).
    • Explanation (Period 2 - Li to Ne): Nuclear charge increases, but shielding from core electrons (1s^2) remains similar. Valence electrons are in the same shell (n=2), similar distance from nucleus. Stronger nuclear attraction leads to higher IE.
    • Drop between Ne and Na: Significant drop because Na's valence electron is in n=3, much farther away and experiencing greater shielding than Ne's valence electrons in n=2. Na is the largest element in Period 3, thus has the lowest IE in its period.
  • Decreases down a group (top to bottom).
    • Explanation (Group 2 - Be, Mg, Ca): Number of core electrons increases, increasing shielding effect. Valence electrons are in shells farther from the nucleus (n=2 for Be, n=3 for Mg, n=4 for Ca). Weaker attraction leads to lower IE.
• Discrepancies to General Trends:
  1. Between Groups 2 and 3 (e.g., Mg vs. Al): The first IE of Al is lower than Mg.
     • Reason: Mg ([Ne]3s^2) has a full 3s subshell. Al ([Ne]3s^23p^1) adds an electron to a 3p subshell, which is slightly farther from the nucleus and higher in energy than 3s. This 3p electron is easier to remove.
  2. Between Groups 15 and 16 (e.g., P vs. S): The first IE of S is lower than P.
     • Reason: P ([Ne]3s^23p^3) has a half-filled 3p subshell (one electron in each of three orbitals), which is relatively stable. S ([Ne]3s^23p^4) has an additional electron that must pair up in a 3p orbital, causing increased spin-pair repulsion. This repulsion makes it easier to remove one electron from S than from P.
• Coulomb's Law Connection:
  • Across a period: Nuclear charge (Q) increases, average distance (r) is similar, increasing coulombic attraction (F \propto Q1 Q2 / r^2), thus higher IE.
  • Down a group: Nuclear charge (Q) increases, but valence shell gets further (r increases significantly), decreasing coulombic attraction, thus lower IE.

Second and Successive Ionization Energies

• Definition: IE2 is the energy to remove an electron from a gaseous X^+ ion (X^+(g) + IE2 \rightarrow X^{2+}(g) + e^-$).
• Trend: Always larger than the preceding IE (IE1 < IE2 < IE_3 \dots) because it's harder to remove an electron from an already positive ion (stronger attraction).
• Significant Jumps: Occur when an electron is removed from a lower, more tightly bound, inner core shell.
  • Example: Lithium (1s^22s^1) vs. Beryllium (1s^22s^2):
    • For Be, both IE1 and IE2 remove electrons from n=2. For Li, IE1 removes from n=2, but IE2 removes from n=1 (core electron).
    • Electrons in n=1 are much closer to the nucleus and experience no shielding, so IE_2 for Li is extremely high compared to Be.
  • Example: Aluminum (Al: [Ne]3s^23p^1):
    • IE_1 (577 \text{ kJ/mol}): removes 3p^1 electron. Result: Al^+ ([Ne]3s^2).
    • IE_2 (1,816 \text{ kJ/mol}): removes 3s^1 electron. Result: Al^{2+} ([Ne]3s^1).
    • IE_3 (2,740 \text{ kJ/mol}): removes 3s^1 electron. Result: Al^{3+} ([Ne]).
    • IE_4 (11,660 \text{ kJ/mol}): removes core electron from n=2. Result: Al^{4+} ([He]2s^22p^5).
    • Observation: The fourth ionization energy is significantly higher, indicating the removal of a core electron from a lower energy level (n=2) that is closer to the nucleus and experiences less shielding.
• Predicting Group Position: The first large "jump" in IE values identifies the number of valence electrons an element has, thus its group in the periodic table.
  • Example: If the jump is between IE2 and IE3, the element has 2 valence electrons and belongs to Group 2.

Periodicity of Other Physical and Chemical Properties

Electron Affinity (EA)

• Definition: The energy change associated with the addition of an electron to a gaseous atom or ion.
  • Equation: X(g) + e^- \rightarrow X^-(g)
  • This is typically the first electron affinity (EA_1).
• Energy Release/Absorption:
  • Negative EA value: Atom releases energy when gaining an electron, forming a stable anion (e.g., chlorine, -349 \text{ kJ/mol}). A more negative value indicates a stronger attraction for the added electron.
  • Positive EA value: Energy must be supplied for the anion to form, meaning the atom doesn't easily form a 1- ion.
• General Trends (with discrepancies):
  • Across a Period (Left to Right): Becomes more negative.
    • Explanation: Nuclear charge increases, but the valence shell remains the same. Coulombic attractions increase, making it easier to capture an electron, leading to more released energy (more negative EA).
    • Shielding stays relatively the same.
  • Down a Group (Top to Bottom): Becomes less negative.
    • Explanation: Nuclear charge increases, but the valence shell's principal quantum number increases. Coulombic attractions decrease as the valence shell is farther from the nucleus, making it harder to capture an electron, leading to less released energy (less negative EA).
    • Shielding increases as atomic radius increases.
• Notable Exceptions:
  1. Group 1 to Group 2: Electron affinity becomes more positive.
     • Reason: In Group 1, the electron is added to an s orbital. In Group 2, the electron is added to a p orbital, which is farther from the nucleus and experiences more effective shielding, resulting in a weaker attraction for the electron.
  2. Group 14 to Group 15: Electron affinity becomes more positive.
     • Reason: In Group 14, the electron is added to an empty p orbital. In Group 15, the electron is added to a p orbital that is already singly occupied. This causes increased electron-electron repulsion, overcoming electron-proton attraction and leading to a weaker (more positive) EA.

Trends in Melting Points

• Explanation Based on Structure and Bonding:
  1. Metals (Groups 1-13, typically before metalloids):
     • Structure: Lattice of cations surrounded by a "sea" of free-moving, delocalized electrons (metallic bonding).
     • Bond Strength: Increases with nuclear charge and number of valence electrons contributed to the electron sea.
     • Melting Point: Relatively high. Increases from left to middle (e.g., Mg > Na).
  2. Metalloids (e.g., Carbon, Silicon):
     • Structure: Giant molecular structure with intricate covalent bonding among all atoms.
     • Bond Strength: Requires a lot of energy to break these extensive covalent bonds.
     • Melting Point: Very high (e.g., Carbon or Silicon are apexes in their periods).
  3. Nonmetals (Groups 16-18, typically after metalloids):
     • Simple Molecular Structures (e.g., O2, Cl2):
       • Bonds: Strong covalent bonds within each molecule.
       • Intermolecular Forces: Weak forces among different molecules.
       • Melting Point: Very low (e.g., nitrogen).
     • Giant Covalent / Molecular Structures (e.g., Diamond - carbon allotrope):
       • Bonds: A large number of atoms covalently bonded together in a network.
       • Melting Point: Extremely high (e.g., Diamond melts at 4,027 \text{°C}).

Trends in Electrical Conductivity

• Explanation Based on Electron Mobility:
  1. Metals (Groups 1-13):
     • Conductivity: High electrical conductivity.
     • Reason: Free-moving, delocalized electrons allow current to flow when an electric potential is applied.
     • Trend: Increases from left to right across the metal section of a period (e.g., \text{Al} > \text{Mg} > \text{Na}) because elements farther to the right donate more electrons to the delocalized pool.
  2. Metalloids and Nonmetals:
     • Conductivity: Poor electrical conductivity.
     • Reason: Their giant molecular or simple molecular structures do not allow for free-flowing valence electrons.

Electronegativity

• Definition: The ability of an atom forming a covalent bond to attract shared electrons to itself.
• Pauling Scale: Most commonly used scale for quantifying electronegativity.
  • Range: From 0.7 (Cesium and Francium) to 4.0$$ (Fluorine).
• General Trends:
  • Increases Across a Period (Group 1 to 17):
    • Explanation: Nuclear charge increases, but the shielding effect remains almost the same. This leads to stronger Coulombic attractions between the nucleus and the shared electrons, increasing electronegativity.
  • Decreases Down a Group:
    • Explanation: Atomic radius and the number of inner shells/subshells increase, thus shielding increases. As electrons are farther from the nucleus and experience greater shielding, they are subject to weaker Coulombic attractions, decreasing electronegativity.
• Exceptions: Occur in transition metals.
• Noble Gases: Generally not included in electronegativity charts as they typically do not form covalent bonds or attract electrons in that manner.