• Periods: There are seven periods in the periodic table, each corresponding to the principal energy level of electrons in the elements. As you move from left to right across a period, elements transition from metallic to non-metallic properties.
• Groups: There are 18 groups in the periodic table. Elements within the same group share similar chemical behaviors due to having the same number of valence electrons.

• Across a Period: Atomic radius decreases from left to right. This is because increasing nuclear charge pulls the electron cloud closer to the nucleus, reducing the atomic size.
• Down a Group: Atomic radius increases as additional electron shells are added, making the atoms larger despite the increased nuclear charge.

For example, lithium (Li) has a larger atomic radius than fluorine (F) despite being in the same period because fluorine has a higher nuclear charge.

• Across a Period: Ionization energy generally increases from left to right due to the decreasing atomic radius and increasing nuclear charge.
• Down a Group: Ionization energy decreases as the atomic radius increases, making it easier to remove an outer electron.

For instance, the ionization energy of neon (Ne) is higher than that of sodium (Na) because Ne has a smaller atomic radius and a higher effective nuclear charge.

• Across a Period: Electronegativity increases from left to right as atoms better attract bonding electrons.
• Down a Group: Electronegativity decreases due to the increasing distance between the nucleus and the bonding electrons.

Chlorine (Cl) is more electronegative than phosphorus (P) because Cl is located to the right of P in the same period.

• Metals: Located on the left and in the center of the periodic table, metals are typically shiny, malleable, ductile, and good conductors of heat and electricity. They tend to lose electrons during chemical reactions.
• Non-Metals: Found on the right side of the table, non-metals are varied in appearance but generally poor conductors of heat and electricity. They tend to gain or share electrons in reactions.
• Metalloids: Positioned along the zigzag line between metals and non-metals, metalloids exhibit intermediate properties.

• Alkali Metals (Group 1): Highly reactive, especially with water, due to their single valence electron which they readily lose.
• Alkaline Earth Metals (Group 2): Less reactive than alkali metals but still react with water and oxygen.
• Halogens (Group 17): Extremely reactive non-metals that readily gain an electron to form negative ions.
• Noble Gases (Group 18): Inert and display very low reactivity due to having a complete valence shell.

• Across a Period: Electron affinity generally increases, indicating a greater tendency to accept electrons.
• Down a Group: Electron affinity decreases as the increased atomic size makes it less favorable to add an electron.

Fluorine has a higher electron affinity compared to magnesium, reflecting its stronger desire to gain an electron.

• Groups Determine Valence Electrons: Elements in the same group have the same number of valence electrons, leading to similar bonding behavior.
• Ionic Bonding: Metals tend to lose valence electrons to form cations, while non-metals gain electrons to form anions.
• Covalent Bonding: Non-metals share valence electrons to achieve stable electron configurations.

• Metals: Typically have high melting and boiling points due to strong metallic bonding.
• Non-Metals: Often have lower melting and boiling points, reflecting weaker intermolecular forces.
• Transition Metals: Exhibit variable melting and boiling points, influenced by their d-electrons.

Mendeleev's periodic law initially ordered elements by atomic mass, but modern periodic law utilizes atomic number for a more accurate organization.

• Across a Period: As $Z$ increases, $Z_{\text{eff}}$ increases, leading to a stronger pull on valence electrons. This results in smaller atomic radii and higher ionization energies.
• Down a Group: Despite the increase in $Z$, the shielding effect from additional inner shells reduces $Z_{\text{eff}}$, leading to larger atomic radii and lower ionization energies.

For example, sodium (Na) has a lower $Z_{\text{eff}}$ compared to magnesium (Mg) in the same period, making Na's outer electron easier to remove.

• Orbital Types: s, p, d, and f orbitals have different shapes and energies, affecting bonding and reactivity.
• Electron Configuration: Determines an element's placement in the periodic table and predicts bonding behavior and reactivity.

Carbon's electron configuration ($1s^2 2s^2 2p^2$) allows for four covalent bonds, leading to its versatility in forming various organic compounds.

• Metal Reactivity: Metals higher in a group (e.g., lithium) are more reactive than those lower in the same group (e.g., potassium).
• Non-Metal Reactivity: Non-metals to the right of the periodic table are generally more reactive, with halogens being highly reactive.
• Acid-Base Behavior: Position in the periodic table can predict acidic or basic properties. Non-metals often form acidic oxides, while metals form basic oxides.

Sulfur dioxide (SO₂), a non-metal oxide, reacts with water to form sulfurous acid (H₂SO₃), showcasing its acidic behavior.

• Aluminum Alloys: Combine aluminum with elements like copper or magnesium to increase strength and resistance to corrosion.
• Steel Production: Iron is alloyed with carbon and other elements to produce steel, which has superior mechanical properties compared to pure iron.

Adding chromium to steel produces stainless steel, which is resistant to rust and staining.

• Lanthanides: Known for their magnetic and phosphorescent properties, used in applications like LEDs and magnets.
• Actinides: Primarily radioactive, with applications in nuclear energy and medicine.

Uranium, an actinide, is widely used as fuel in nuclear reactors due to its radioactive properties.

• Superheavy Elements: Elements beyond uranium (atomic number 92) are synthetic and have very short half-lives.
• Island of Stability: A theoretical region in the periodic table where superheavy elements might exhibit greater stability.

Element 118, oganesson (Og), is the heaviest element currently recognized, exhibiting properties that challenge existing periodic trends.

• Semiconductors: Elements like silicon and germanium, positioned in the p-block, are essential in electronics.
• Rare Earth Metals: Lanthanides are critical in producing strong permanent magnets used in various technologies.

Silicon's position in group 14 enables it to form stable covalent bonds, making it ideal for semiconductor applications.

• Heavy Metals: Elements like lead and mercury (found in specific groups) have significant environmental and health impacts due to their toxicity.
• Greenhouse Gases: Non-metals such as carbon and sulfur contribute to greenhouse gas emissions, influencing climate change.

Understanding the reactivity of carbon (group 14) helps in managing carbon emissions and developing strategies for carbon capture.

• Periodic Trends Formulas: Equations like Slater's rules help calculate effective nuclear charge.
• Quantum Chemical Calculations: Advanced computations predict behaviors of elements in various chemical environments.

Density Functional Theory (DFT) is a quantum mechanical modeling method used to investigate the electronic structure of atoms and molecules.

• Predicting Reactivity of Group 1 Elements: Alkali metals like potassium (K) are highly reactive, especially with water, due to their single valence electron and large atomic radius.
• Understanding Noble Gas Stability: Helium (He) and neon (Ne) are inert due to their complete valence shells, making them non-reactive under standard conditions.

Potassium reacts vigorously with water to form potassium hydroxide and hydrogen gas, illustrating the high reactivity predicted by its group position.

• The periodic table's arrangement allows prediction of elemental properties based on position.
• Trends such as atomic radius, ionization energy, and electronegativity vary systematically across periods and groups.
• Understanding valence electrons is crucial for predicting chemical bonding and reactivity.
• Advanced concepts like effective nuclear charge and quantum models deepen the predictive power of the periodic table.
• Applications of periodic trends span material science, environmental science, and beyond.