Elements, Atoms, and the Periodic Table

Fundamentals of Elements and Atoms

• Element Definition: A fundamental substance that cannot be broken down by chemical means into a simpler substance. Elements serve as the primary building blocks of all matter. They can occur naturally in nature or be synthetically produced in laboratory environments.

• Atom Definition: The smallest unit of an element that retains the chemical properties and behavior of that element.

  • Atoms consist of smaller subatomic particles (protons, neutrons, and electrons).

  • Subatomic particles in isolation do not possess the chemical properties of the element.

• Total Elements: There are currently $118$ known elements, $88$ of which occur naturally on Earth.

• Chemical Symbols: Each element is abbreviated using a standard one- or two-letter symbol (e.g., $\text{H}$, $\text{He}$, $\text{Na}$).

The Periodic Table of Elements

• History: Designed by Dmitri Mendeleev in $1869$ to organize elements systematically according to their physical and chemical properties.

• Structural Organization of the Periodic Table:

  • Periods: Horizontal rows on the periodic table, numbered $1$ through $7$. The period number corresponds to the highest principal energy level ($n$) occupied by electrons in an atom of that element.

  • Groups (Families): Vertical columns on the periodic table, labeled either using numbers ($1$–$18$) or traditional American system designations ($1\text{A}$–$8\text{A}$ for main group elements, and $\text{B}$ designations for transition metals).

  • Main Group (Representative) Elements: Elements located in Groups $1\text{A}$ through $8\text{A}$ (Groups $1$, $2$, and $13$–$18$).

  • Transition Elements (Transition Metals): Elements spanning Groups $3\text{B}$ through $2\text{B}$ (Groups $3$–$12$), filling the $d$-orbital subshell.

  • Inner Transition Elements: Located below the main body of the periodic table, consisting of two series filling the $f$-orbital subshell:

    • Lanthanide Series: Elements $58$ through $71$ ($\text{Ce}$ to $\text{Lu}$).

    • Actinide Series: Elements $90$ through $103$ ($\text{Th}$ to $\text{Lr}$).

Abundance and Classification of Matter

• Elemental Abundance in the Earth's Crust, Oceans, and Atmosphere:

  • Ten elements account for almost $99$% of the total mass of the Earth's crust, seawater, and atmosphere.

  • Oxygen is the most abundant element, accounting for about $20$% of the Earth's atmosphere and present in nearly all rocks, sand, and soil.

• Elemental Abundance in the Human Body:

*   Major constituents: Oxygen ($65$%), Carbon ($18$%), Hydrogen ($10$%), Nitrogen ($3$%), Calcium ($1.4$%), Phosphorus ($1$%).
*   Trace elements: Minor amounts of elements like Chromium ($\text{Cr}$) and Copper ($\text{Cu}$) are critical for essential biological functions.

• Classification of Elements by Physical Properties:

  • Metals:

    • State at Room Temperature: Solid (except Mercury, $\text{Hg}$, which is liquid).

    • Appearance: High luster (shiny).

    • Conductivity: Excellent conductors of heat and electricity.

    • Malleability: Can be hammered or rolled into thin sheets.

    • Ductility: Can be drawn into fine wires.

    • Melting Point & Density: High melting points and high densities.

    • Reactivity: React readily with nonmetals to form chemical compounds; rarely combine chemically with other metals.

    • Free State Occurrence: Gold ($\text{Au}$), Silver ($\text{Ag}$), Copper ($\text{Cu}$), and Platinum ($\text{Pt}$) (the noble metals) have low reactivity and are frequently found uncombined in nature.

    • Alloys: Homogeneous mixtures of two or more metals (e.g., brass, bronze, steel, coinage metals).

  • Nonmetals:

    • Appearance: Lack luster (dull surface).

    • Melting Point & Density: Relatively low melting points and low densities.

    • Conductivity: Poor conductors of heat and electricity (insulators).

    • Reactivity: Combine with each other via covalent bonds to form molecular compounds; combine with metals via ionic bonds to form ionic compounds.

  • Metalloids (Semimetals):

    • Properties: Intermediate characteristics between metals and nonmetals.

    • Periodic Location: Positioned along the diagonal stair-step line separating metals and nonmetals.

    • Key Examples: Boron ($\text{B}$), Silicon ($\text{Si}$), Germanium ($\text{Ge}$), Arsenic ($\text{As}$), Antimony ($\text{Sb}$), Tellurium ($\text{Te}$), and Polonium ($\text{Po}$).

    • Applications: Essential materials used as semiconductors in modern electronic devices.

• Diatomic Elements:

  • Definition: Elements that exist naturally as molecules containing exactly two atoms bound together.

  • Mnemonic: HOFBrINCl (Hydrogen, Oxygen, Fluorine, Bromine, Iodine, Nitrogen, Chlorine).

*   *Important Distinction*: When present inside a chemical compound such as water ($\text{H}_2\text{O}$), hydrogen and oxygen exist as individual atoms bound within the compound structure, not as diatomic gas molecules.

Physical and Chemical Properties and Changes

• Physical Properties: Inherent characteristics of a substance that can be observed or measured without altering its fundamental chemical composition.

  • Examples: Color, odor, taste, state of matter (solid, liquid, gas), density, melting point, boiling point.

• Chemical Properties: Characteristics describing the ability of a substance to undergo chemical reactions with other substances or decompose into simpler substances.

  • Example Equation: $2\text{Na}\text{(s)} + \text{Cl}_2\text{(g)} \rightarrow 2\text{NaCl}\text{(s)}$

• Physical Change: A transformation that alters physical properties or state of matter without producing any change in chemical composition. No new chemical substances are created.

  • Example: Sawing wood changes the shape and size of the wood, but the sawdust and pieces remain chemically identical to wood.

• Chemical Change: A transformation in which one or more initial substances are converted into entirely new substances with different physical and chemical properties and compositions.

  • Example: Heating shiny copper wire in air turns the surface black due to the formation of copper(II) oxide:         2\text{Cu}\text{(s)} + \text{O}_2\text{(g)} \buildrel \text{\buildrel \text{$\begin{array}{c}\\[-1em]\Delta\end{array}$} \over \rightarrow}} 2\text{CuO}\text{(s)}

    • Before heating: $1.000\text{ g}$ of $100$% copper ($\text{Cu}$) metal wire.

    • After heating: $1.251\text{ g}$ of black copper(II) oxide ($\text{CuO}$), consisting of $79.9$% copper and $20.1$% oxygen by mass.

• Summary of Common Physical and Chemical Processes:

  • Rusting of iron: Chemical Change (shiny metal turns into reddish-brown rust).

  • Boiling of water: Physical Change (liquid water converts to gaseous vapor).

  • Burning of sulfur in air: Chemical Change (yellow solid sulfur transforms into choking gaseous sulfur dioxide, $\text{SO}_2$).

  • Boiling of an egg: Chemical Change (liquid egg white and yolk denature and solidify).

  • Combustion of gasoline: Chemical Change (liquid hydrocarbons burn to form gaseous carbon monoxide, carbon dioxide, and water vapor).

  • Digestion of food: Chemical Change (complex food polymers break down into liquid nutrients and waste products).

  • Sawing of wood: Physical Change (large timber converted into smaller pieces and sawdust).

  • Burning of wood: Chemical Change (combustion of wood yields ash, carbon dioxide, and water vapor).

  • Heating of glass: Physical Change (solid glass softens, becomes pliable, and alters shape without decomposing).

Chemical Formulas, Equations, and Fundamental Laws

• Compounds: Pure substances containing two or more distinct elements chemically combined in fixed, definite proportions by mass.

  • Can be decomposed into simpler substances or elements via chemical reactions.

  • Elements in compounds are present in exact whole-number atom ratios.

  • Over $50\text{ million}$ chemical compounds are currently known.

• Types of Compounds:

*   **Molecular Compounds**:
    *   Formed between nonmetal elements.
    *   Held together by covalent chemical bonds (shared electrons).
    *   Smallest individual representative particle: **Molecule** (the smallest uncharged unit of a compound that retains its identity).
*   **Ionic Compounds**:
    *   Formed between metals and nonmetals.
    *   Held together by strong electrostatic attractive forces between positively charged cations and negatively charged anions.
    *   Do not consist of isolated molecules; exist as extended three-dimensional crystal lattices.

• Ions: Charged atoms or groups of atoms.

  • Cation: A positively charged ion formed when a neutral atom loses one or more electrons.

  • Anion: A negatively charged ion formed when a neutral atom gains one or more electrons.

• Unique Physical Properties of Compounds: Compounds composed of identical elements in different ratios display distinct properties:

  • Water ($\text{H}_2\text{O}$): Clear, colorless liquid; Boiling point = $100\text{ }^\text{o}\text{C}$; Density = $1.00\text{ g/mL}$.

  • Hydrogen Peroxide ($\text{H}_2\text{O}_2$): Pale blue liquid; Boiling point = $150\text{ }^\text{o}\text{C}$; Density = $1.44\text{ g/mL}$.

• Chemical Formula: Symbolic representation showing the elements present in a compound and the numerical ratio of their atoms using subscript numbers.

• Fundamental Laws of Chemical Composition:

  • Law of Conservation of Matter: Matter can neither be created nor destroyed during a physical or chemical process.

  • Law of Definite Composition (Law of Definite Proportions): A specific chemical compound always contains its constituent elements in exact, fixed mass proportions regardless of the sample source or method of preparation.

    • Water ($\text{H}_2\text{O}$): Always contains $11.2$% Hydrogen and $88.8$% Oxygen by mass (Mass Ratio $\text{O : H} = 7.93 : 1$).

    • Hydrogen Peroxide ($\text{H}_2\text{O}_2$): Always contains $5.9$% Hydrogen and $94.1$% Oxygen by mass.

  • Law of Multiple Proportions: When two elements combine to form more than one distinct compound, the masses of one element that combine with a fixed mass of the second element are in ratios of small whole numbers.

• Chemical Equations: Expressions representing a chemical reaction.

  • Reactants: Starting materials written on the left side.

  • Products: Newly formed substances written on the right side.

  • Arrow ($\rightarrow$): Represents "produces" or "yields", pointing toward products.

  • Decomposition of water: $2\text{H}_2\text{O}\text{(l)} \rightarrow 2\text{H}_2\text{(g)} + \text{O}_2\text{(g)}$

  • Formation of salt: $2\text{Na} + \text{Cl}_2 \rightarrow 2\text{NaCl}$

Atomic Structure and Subatomic Particles

• Historical Evolution of Atomic Theory:

  • Empedocles (Greek philosopher): Proposed matter consists of four basic elements: earth, air, water, and fire.

  • Democritus (Greek philosopher): Proposed matter is composed of minute, indivisible particles termed atoms ("atomos").

  • Aristotle: Rejected Democritus' atomic model and supported Empedocles, suppressing atomic theory acceptance for over $2000\text{ years}$.

  • John Dalton ($1800\text{s}$ Atomic Model):

    1. Elements are composed of extremely small, indivisible particles called atoms.

    2. All atoms of a given element are identical in mass, size, and properties.

    3. Atoms of different elements possess different masses and physical properties.

    4. Chemical compounds form when atoms of different elements combine.

    5. Atoms combine in simple, whole-number ratios to form compounds.

    6. Atoms of two elements may combine in different numerical ratios to yield distinct compounds.

  • Modern Revisions to Dalton's Postulates:

    1. Atoms can be split into subatomic components under nuclear reactions.

    2. Not all atoms of the same element have identical masses (existence of isotopes).

    3. Atoms are divisible into subatomic particles.

• Properties of Electric Charge:

  1. Electric charges are designated as either positive ($+$) or negative ($-$).

  2. Opposite charges attract each other; like charges repel each other.

  3. Charge can be transferred between objects via direct contact or induction.

  4. The electrostatic force ($F$) between charged particles is inversely related to the distance between them.

• Key Historical Discoveries in Atomic Structure:

  • Michael Faraday: Discovered electrolytes (compounds that conduct electricity when dissolved in water) and observed that dissolved chemical compounds decompose into elements at charged electrodes.

  • Svante Arrhenius: Expanded Faraday's work, postulating that salts like $\text{NaCl}$ dissociate in water into positive cations ($\text{Na}^+$) and negative anions ($\text{Cl}^-$).

  • George Johnstone Stoney: Proposed the existence of the fundamental unit of electrical charge associated with atoms and named it the electron.

  • J. J. Thomson: Confirmed the physical existence of electrons experimentally. Proposed the "Plum Pudding" model: negatively charged electrons embedded within a uniform sphere of positive charge.

  • Ernest Rutherford ($1911$ Gold Foil Experiment):

    *   Bombarded thin gold foil with high-energy alpha particles ($\alpha$, positively charged helium ions $\text{He}^{2+}$).
    *   Observations: Most alpha particles passed directly through undeflected; a small fraction were deflected at sharp angles, and very few bounced straight back.
    *   Conclusions:
        1. The vast majority of an atom is open, empty space.
        2. An atom contains a tiny, extremely dense, positively charged center called the **nucleus**.
        3. Protons and neutrons are packed inside the nucleus, while electrons move throughout the surrounding empty space.
        4. Nuclear scale: Atom diameter = $10^{-8}\text{ cm}$ ($0.1$–$0.5\text{ nm}$); Nucleus diameter = $10^{-13}\text{ cm}$.

• Subatomic Particles Summary Table:

• Fundamental Atomic Definitions:

  • Atomic Number ($Z$): The number of protons contained in the nucleus of an atom. Unique to each element; defines elemental identity.

  • Mass Number ($A$): The total sum of protons and neutrons in the nucleus of a specific atom.         $\text{Mass Number }(A) = \text{Protons } + \text{Neutrons}$         $\text{Number of Neutrons } = A - Z$

Atomic Mass, Isotopes, and Abundance Calculations

• Isotopes: Atoms of the same chemical element possessing the exact same atomic number ($Z$, number of protons) but different numbers of neutrons, resulting in different mass numbers ($A$).

• Isotope Symbol Notation: $^{A}_{Z}\text{E}$, where $\text{E}$ is the element symbol, $A$ is the mass number, and $Z$ is the atomic number.

• Isotopes of Hydrogen:

*   *Protium* ($^{1}_{1}\text{H}$): $1\text{ proton}$, $0\text{ neutrons}$, $1\text{ electron}$.
*   *Deuterium* ($^{2}_{1}\text{H}$ or $\text{D}$): $1\text{ proton}$, $1\text{ neutron}$, $1\text{ electron}$.
*   *Tritium* ($^{3}_{1}\text{H}$ or $\text{T}$): $1\text{ proton}$, $2\text{ neutrons}$, $1\text{ electron}$.

• Atomic Mass Unit (amu):

  • Standard unit of mass defined as exactly $\frac{1}{12}$ the mass of a single carbon-12 ($^{12}_{6}\text{C}$) atom.

  • Conversion factor: $1\text{ amu} = 1.6606 \times 10^{-24}\text{ g}$.

• Atomic Mass (Average Atomic Mass): The weighted average mass of all naturally occurring isotopes of an element based on relative abundance.     $\text{Average Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})$

• Worked Example 1 (Copper):

  • Copper ($\text{Cu}$) natural isotopes: $^{63}_{29}\text{Cu}$ ($62.9298\text{ amu}$, $69.09$% abundance) and $^{65}_{29}\text{Cu}$ ($64.9278\text{ amu}$, $30.91$% abundance).

  • Calculation:         $\text{Average Mass} = (62.9298\text{ amu} \times 0.6909) + (64.9278\text{ amu} \times 0.3091)$         $\text{Average Mass} = 43.4782\text{ amu} + 20.0692\text{ amu} = 63.55\text{ amu}$

  • Most abundant isotope: $^{63}\text{Cu}$, because the average atomic mass ($63.55\text{ amu}$) is closer to $63$ than $65$

• Worked Example 2 (Silver):

  • Silver ($\text{Ag}$) natural isotopes: Mass $106.9041\text{ amu}$ ($51.82$% abundance) and Mass $108.9047\text{ amu}$ ($48.18$% abundance).

  • Calculation:         $\text{Average Mass} = (106.9041\text{ amu} \times 0.5182) + (108.9047\text{ amu} \times 0.4818)$         $\text{Average Mass} = 55.3977\text{ amu} + 52.4703\text{ amu} = 107.8680\text{ amu}$

Electromagnetic Radiation and the Bohr Model

• Wave Properties of Electromagnetic Radiation:

  • Wavelength ($\lambda$): Distance between consecutive wave crests or troughs.

  • Frequency ($ u$): Number of wave cycles passing a fixed point per second (measured in $\text{s}^{-1}$ or $\text{Hz}$).

  • Speed of Light ($c$): Constant propagation velocity in vacuum ($c = 3.00 \times 10^8\text{ m/s}$).         $c = \lambda \nu$

• Electromagnetic Spectrum Range:

*   Order from shortest wavelength (highest energy/frequency) to longest wavelength (lowest energy/frequency):
    1. Gamma rays ($10^{-12}\text{ m}$)
    2. X-rays ($10^{-10}\text{ m}$)
    3. Ultraviolet light ($10^{-8}\text{ m}$)
    4. Visible light ($4 \times 10^{-7}\text{ m}$ to $7 \times 10^{-7}\text{ m}$ / $400$–$700\text{ nm}$)
    5. Infrared light ($10^{-4}\text{ m}$)
    6. Microwaves ($10^{-2}\text{ m}$)
    7. Radio waves ($1\text{ m}$ to $10^4\text{ m}$)

• Atomic Emission Line Spectra:

  • Passing light emitted by excited gas atoms through a prism or spectroscope produces discrete bright line emission spectra (fingerprint of an element).

  • Visible line spectrum of Hydrogen: Discrete lines at $410\text{ nm}$ (violet), $434\text{ nm}$ (blue), $486\text{ nm}$ (green), and $656\text{ nm}$ (red).

• Niels Bohr Model of the Atom:

  • Electrons move around the nucleus only in discrete, circular quantized energy orbits.

  • Ground State: The lowest stable energy level occupied by an electron ($n = 1$).

  • Excited State: A higher energy orbit occupied when an electron absorbs a discrete quantum of energy.

  • Emission Process: When an excited electron drops back down to a lower energy level, energy is released as a photon of light matching the precise energy difference between orbits.

  • Limitation: Bohr's model explained line spectra for hydrogen perfectly, but broke down completely when applied to multi-electron systems.

Quantum Mechanics and Electron Configurations

• Development of Modern Quantum Theory:

  • Louis de Broglie ($1924$): Proposed dual particle/wave nature of matter; microscopic particles like electrons exhibit wave characteristics.

  • Erwin Schrödinger ($1926$): Developed wave equations describing electrons as 3D standing waves, establishing quantum mechanics.

• Orbitals: Regions of space around the nucleus where there is a high probability ($\approx 90$%) of finding an electron. Replaces Bohr's fixed 2D orbits.

• Quantum Numbers & Subshells:

  • Principal Quantum Number ($n$): Main energy level ($n = 1, 2, 3, 4, 5, 6, 7$). Higher $n$ means greater distance from nucleus and higher energy.

  • Subshells ($l$):

    • $s$ orbital: Spherical shape; lowest relative energy; $1$ orbital per shell; holds a maximum of $2\text{ electrons}$.

    • $p$ orbital: Dumbbell/figure-8 shape ($p_x, p_y, p_z$); $3$ orbitals per shell; holds a maximum of $6\text{ electrons}$.

    • $d$ orbital: Four-leaf clover shape ($d_{xz}, d_{xy}, d_{yz}, d_{z^2}, d_{x^2-y^2}$); $5$ orbitals per shell; holds a maximum of $10\text{ electrons}$.

    • $f$ orbital: Complex geometry; highest relative energy; $7$ orbitals per shell; holds a maximum of $14\text{ electrons}$.

• Periodic Table Subshell Blocks:

*   $s$

-block: Groups $1\text{A}$ and $2\text{A}$, plus Helium ($\text{He}$). * $p$ -block: Groups $3\text{A}$ through $8\text{A}$. * $d$ -block: Transition Metals (Groups $3\text{B}$ through $2\text{B}$). * $f$ -block: Inner Transition Elements (Lanthanides $4f$ and Actinides $5f$).

• Electron Configuration Notation: Standard method for detailing subshell occupancy in an atom ($n l^\text{number of electrons}$).

  • Hydrogen ($\text{H}$): $1s^1$

  • Abbreviated Noble Gas Notation: Replaces inner-core configuration with preceding noble gas symbol in brackets (e.g., Sodium, $\text{Na}$: $[\text{Ne}] 3s^1$).

• Order of Electron Loss During Cation Formation:

  1. Electrons lost first from outer energy level unfilled subshells.

  2. Electrons lost next from outer energy level filled subshells.

  3. Electrons lost next from inner energy level unfilled subshells.

  4. Electrons lost last from inner energy level filled subshells (rare).

• Valence Electrons:

  • Electrons occupying the outermost principal energy level (highest $n$ shell).

  • Play the dominant role in chemical bonding and chemical reactivity.

  • For main group elements (Groups $1\text{A}$–$8\text{A}$), the Group Number equals the number of valence electrons (Exception: Helium has $2$ valence electrons).

• Lewis Electron-Dot Symbols:

  • Valence electrons represented as dots placed around four sides of the atomic symbol.

  • Single dots placed on sides for $1$ to $4$ valence electrons; dots paired up when valence electrons exceed

  • Visual Representation of Electron-Dot Symbols:

    ``` Hydrogen (1 e-): H ·

                     ·
    

    Carbon (4 e-): · C · ·

                     ··
    

    Oxygen (6 e-): : O · ·

                     ··
    

    Chlorine (7 e-): : Cl : ··         ```

Periodic Trends

• Atomic Size (Atomic Radius):

  • Group Trend (Vertical): Increases moving down a column/group. As the principal energy level (nn) increases, electrons occupy orbitals farther from the nucleus, increasing the atomic size.

  • Period Trend (Horizontal): Decreases moving left to right across a row/period. As protons are added to the nucleus, the increasing positive nuclear charge pulls the valence electrons closer to the nucleus.

• Ionization Energy:

  • Definition: The minimum energy required to remove an electron from a neutral atom in the gaseous state (Na+energy→Na++e−Na+energy→Na++e−).

  • Group Trend (Vertical): Decreases moving down a column/group because valence electrons are farther from the nucleus and experience weaker electrostatic attraction.

  • Period Trend (Horizontal): Increases moving left to right across a row/period because increased nuclear charge holds electrons more tightly, requiring more energy to remove an electron.