§ C-11 Periodic Table of Elements (118 Elements): Atomic Radius rₐt, Ionization I₁ & χ (Grade 8–11 · Periodic Trends)
Complete 3D Periodic Table of all 118 chemical elements (Periods 1–7, Groups 1–18, s-, p-, d-, and f-blocks: Lanthanides & Actinides), atomic radius rₐt, ionization energy I₁ & electronegativity χ. Moving left to right across a period, effective nuclear charge Zₑff = Z − σ rises steadily, contracting the valence shell, while stepping down to a new period adds a new principal electron shell.
Theory Summary & Scientific Mechanism
In modern quantum mechanics, the Periodic Law states that the physical and chemical properties of elements vary periodically with their atomic number Z, driven by the periodic recurrence of outer-shell valence electron configurations (ns¹ … ns² np⁶).
The governing parameter behind atomic radius rₐt, first ionization energy I₁, and Pauling electronegativity χ is Slater’s effective nuclear charge Zₑff = Z - σ, where σ is the shielding constant of core electrons. Moving left to right across a period (n = const), electrons enter the same principal shell and shield one another poorly (Δ σ ≈ 0.35), causing Zₑff to increase by ≈ 0.65 per step. Stronger electrostatic attraction pulls the valence shell inward (rₐt ↓) while increasing ionization energy I₁ and electronegativity χ.
Moving down a main group adds new principal electron shells (n = 1, 2, 3, 4…), increasing atomic radius rₐt and decreasing I₁ and χ, which explains the increasing metallic reactivity of alkali metals from Li to K and Cs.
Everyday Analogy
Moving left to right across a period is like strengthening a central magnet while keeping the same shell ring: higher effective nuclear charge Zₑff pulls the shell inward (smaller atomic radius) and holds electrons more tightly (higher ionization energy)!
Interactive Question & Derivation
How do atomic radius rₐt, first ionization energy I₁, and electronegativity χ change as you move from left to right across a single period of the Periodic Table?
- A: Atomic radius rₐt decreases (due to rising effective nuclear charge Zₑff = Z - σ pulling the shell inward), while ionization energy I₁ and electronegativity χ increase
- B: Atomic radius rₐt increases and ionization energy I₁ decreases as electrons are added
- C: All three properties (rₐt, I₁, χ) remain constant across a period
Study Hint: Across a period, shell number n is constant while effective nuclear charge Zₑff = Z - σ increases, shrinking atomic radius rₐt and raising ionization energy I₁ and electronegativity χ.
Proof & Explanation: Across a period, electrons enter the same outer shell n and shield one another imperfectly, so Slater’s effective nuclear charge Zₑff = Z - σ increases. Stronger Coulomb attraction contracts the valence shell (rₐt decreases, including d-block and 4f lanthanide contraction) and binds valence electrons more tightly (I₁ and χ increase).
Key Equations & 3D Simulation Parameters
Zₑff = Z - σ, rₐt ≈ (n² a₀)/(Zₑff), I₁ ∝ (Zₑff²)/(n²)
- Atomic number Z (all 118 elements): 1 … 118 (default: 26)
- Period n (1–7, electron shells): 1 … 7 (default: 4)
- IUPAC Group (1–18: s-, d-, p-blocks): 1 … 18 (default: 8)
- 3D matrix relief (1=Radius rₐt, 2=Ionization I₁, 3=Electroneg. χ): 1 … 3 (default: 1)