Atomic Structure, Quantum Numbers, and Valence Electrons

Fundamentals of Atomic Structure and Nuclear Notation

• Atomic Architecture and Subatomic Particles:

  • The atomic number, denoted by the symbol $Z$, represents the total count of protons contained within the atomic nucleus. This fundamental integer defines the chemical identity of an element.
  • The mass number, designated by the symbol $A$, equals the sum total of all nucleons (protons and neutrons) residing in the nucleus:         $A = Z + N$
  • The neutron number, designated by $N$ or $n^{\circ}$, is calculated directly by subtracting the atomic number from the mass number:         $N = A - Z$
  • In any electrically neutral atom, the number of negatively charged extranuclear electrons ($e^{-}$) equals the number of positively charged nuclear protons ($p$), such that:         $\text{Number of electrons} = \text{Number of protons} = Z$

• Standard Isotopic Representation Notation:

  • The universal complete typographic notation for an atomic nucleus (nuclide) is structured as:         ${}_{Z}^{A}\text{X}$
  • In this formal notation:
    • $\text{X}$ represents the chemical symbol of the element.
    • $A$ appears as the upper left superscript denoting the total nucleon count (mass number).
    • $Z$ appears as the lower left subscript denoting the nuclear charge / atomic number.

• Nuclide Analysis and Subatomic Particle Quantifications (Colegio Santa María la Real Curriculum):

  • Bromine Species (${}_{35}^{82}\text{Br}$):
    • Chemical Identity: Bromine ($\text{Br}$)
    • Atomic Number ($Z$): $35$
    • Mass Number ($A$): $82$
    • Number of Protons: $35$
    • Number of Neutrons: $82 - 35 = 47$
    • Number of Electrons (neutral ground state): $35$
  • Iron Divalent Cation (${}_{26}^{58}\text{Fe}^{2+}$):
    • Chemical Identity: Iron ($\text{Fe}$)
    • Atomic Number ($Z$): $26$
    • Mass Number ($A$): $58$
    • Number of Protons: $26$
    • Number of Neutrons: $58 - 26 = 32$
    • Number of Electrons: $26 - 2 = 24$ (due to the loss of $2$ valence electrons)
  • Scandium ($\text{Sc}$):
    • Chemical Identity: Scandium ($\text{Sc}$)
    • Atomic Number ($Z$): $21$
    • Number of Protons: $21$
    • Number of Neutrons: $30$
    • Derived Mass Number ($A$): $21 + 30 = 51$
    • Number of Electrons: $21$
  • Hydrogen / Light Nucleus Exercise Parameter:
    • Number of Protons: $1$
    • Number of Neutrons: $30$
  • Silver Species (${}_{47}\text{Ag}$):
    • Chemical Identity: Silver ($\text{Ag}$)
    • Atomic Number ($Z$): $47$
    • Associated Table Mass / Parameter Value: $58$
    • Number of Protons: $47$
  • Oxygen Species ($\text{O}$):
    • Chemical Identity: Oxygen ($\text{O}$)
    • Number of Protons: $8$
    • Number of Neutrons: $9$
    • Derived Mass Number ($A$): $8 + 9 = 17$
    • Number of Electrons: $8$
  • Carbon Species (${}_{6}^{14}\text{C}$):
    • Chemical Identity: Carbon ($\text{C}$)
    • Atomic Number ($Z$): $6$
    • Mass Number ($A$): $14$
    • Number of Protons: $6$
    • Number of Neutrons: $14 - 6 = 8$
    • Number of Electrons: $6$
  • Nitride Anion (${}_{7}^{15}\text{N}^{3-}$):
    • Chemical Identity: Nitrogen ($\text{N}$)
    • Atomic Number ($Z$): $7$
    • Mass Number ($A$): $15$
    • Number of Protons: $7$
    • Number of Neutrons: $15 - 7 = 8$
    • Number of Electrons: $7 + 3 = 10$ (due to the addition of $3$ electrons)

Cations, Anions, and Material Structure

• Ionic Classifications and Governing Principles:

  • An ion is an atom or molecule with a net electric charge resulting from the gain or loss of one or more electrons.
  • Cations: Positively charged ionic species produced when a neutral atom loses electrons. The net positive charge occurs because the number of nuclear protons exceeds the number of extranuclear electrons ($p > e$).
  • Anions: Negatively charged ionic species produced when a neutral atom gains electrons. The net negative charge occurs because the number of extranuclear electrons exceeds the number of nuclear protons ($e > p$).
  • Mathematical Relations for Ionic Charge:$\text{Net Charge} = p - e$$\text{Number of Electrons } (e) = Z - (\text{Net Charge})$$\text{Number of Neutrons } (n^{\circ}) = A - Z$

• Ionic Species Breakdown (Instruction by Profa. Jesica Patricia Flores Fernández):

  • Sodium Ion ($\text{Na}^{+}$):
    • Ion Type: Cation (catión)
    • Atomic Number ($Z$): $11$
    • Net Charge: $+1$
    • Proton Count ($p$): $11$
    • Electron Count ($e$): $11 - 1 = 10$
  • Sulfide Ion ($\text{S}^{2-}$):
    • Ion Type: Anion (anión)
    • Atomic Number ($Z$): $16$
    • Net Charge: $-2$
    • Proton Count ($p$): $16$
    • Electron Count ($e$): $16 + 2 = 18$ (recorded reference parameter: $16$)
  • Magnesium Ion ($\text{Mg}^{2+}$):
    • Ion Type: Cation
    • Atomic Number ($Z$): $12$
    • Net Charge: $+2$
    • Proton Count ($p$): $12$
    • Electron Count ($e$): $12 - 2 = 10$
  • Gallium Ion ($\text{Ga}^{3+}$):
    • Ion Type: Cation
    • Mass Number ($A$): $70$
    • Atomic Number ($Z$): $31$
    • Proton Count ($p$): $31$
    • Neutron Count ($n^{\circ}$): $70 - 31 = 39$
    • Electron Count ($e$): $31 - 3 = 28$
  • Selenide Ion ($\text{Se}^{2-}$):
    • Ion Type: Anion
    • Atomic Number ($Z$): $34$
    • Net Charge: $-2$
    • Proton Count ($p$): $34$
    • Electron Count ($e$): $34 + 2 = 36$
  • Aluminum Ion ($\text{Al}^{3+}$ / $\text{Al}^{+3}$):
    • Ion Type: Cation
    • Atomic Number ($Z$): $13$
    • Net Charge: $+3$
    • Proton Count ($p$): $13$
    • Electron Count ($e$): $13 - 3 = 10$
  • Bromide Ion ($\text{Br}^{-}$):
    • Ion Type: Anion
    • Atomic Number ($Z$): $35$
    • Net Charge: $-1$
    • Proton Count ($p$): $35$
    • Electron Count ($e$): $35 + 1 = 36$
  • Francium Ion ($\text{Fr}^{+}$):
    • Ion Type: Cation
    • Associated Core / Proton Value Recorded: $86$
  • Chloride Ion ($\text{Cl}^{-}$):
    • Ion Type: Anion
    • Atomic Number ($Z$): $17$
    • Net Charge: $-1$
    • Proton Count ($p$): $17$
    • Electron Count ($e$): $17 + 1 = 18$
  • Iodide Species ($\text{I}^{-}$):
    • Ion Type: Anion
    • Atomic Number ($Z$): $53$
    • Net Charge: $-1$
  • Strontium Ion ($\text{Sr}^{2+}$):
    • Ion Type: Cation
    • Associated Recorded Parameter: $39$
    • Atomic Number ($Z$): $38$
  • Boron Ion ($\text{B}^{3+}$ / $\text{B}^{+3}$):
    • Ion Type: Cation
    • Atomic Number ($Z$): $5$
    • Protons ($p$): $5$
    • Associated Numerical Values Recorded: $5$, $5$, $10$, $10$

Quantum Numbers and Electronic Structure of Elements

• Theoretical Foundations of the Quantum Numbers:
  • The electronic state of an electron in an atom is completely specified by four quantum numbers:
    • Principal Quantum Number ($n$): Determines the main electron shell and primary energy level of the orbital. Permissible integer values: $n = 1, 2, 3, 4, \dots$
    • Azimuthal / Angular Momentum Quantum Number ($l$): Dictates the three-dimensional geometric shape of the subshell orbital. For a given shell $n$, the permissible values are integers where $0 \le l \le n - 1$:
      • $l = 0 \rightarrow s$ subshell (spherical)
      • $l = 1 \rightarrow p$ subshell (dumbbell-shaped / polar)
      • $l = 2 \rightarrow d$ subshell (cloverleaf)
      • $l = 3 \rightarrow f$ subshell (complex fundamental)
    • Magnetic Quantum Number ($m$ or $m_l$): Describes the orientation of the orbital in space relative to an applied magnetic field. Permissible integer values range symmetrically around zero:             $-l \le m_l \le +l$
    • Spin Quantum Number ($s$ or $m_s$): Quantifies the intrinsic spin angular momentum projection of the electron along the quantization axis. Permissible values:             $m_s = +\frac{1}{2} \quad \text{or} \quad m_s = -\frac{1}{2}$

• Elemental Inventory for Quantum Determination (Catalog Series 11 to 20):
  • 11. Hydrogen (Hidrógeno):
    • Chemical Symbol: $\text{H}$
    • Electron Configuration: $1s^1$
    • Differentiating Electron Quantum Set: $n = 1$, $l = 0$, $m_l = 0$, $m_s = +\frac{1}{2}$
  • 12. Helium (Helio):
    • Chemical Symbol: $\text{He}$
    • Electron Configuration: $1s^2$
    • Differentiating Electron Quantum Set: $n = 1$, $l = 0$, $m_l = 0$, $m_s = -\frac{1}{2}$
  • 13. Lithium (Litio):
    • Chemical Symbol: $\text{Li}$
    • Electron Configuration: $1s^2\,2s^1$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 0$, $m_l = 0$, $m_s = +\frac{1}{2}$
  • 14. Beryllium (Berilio):
    • Chemical Symbol: $\text{Be}$
    • Electron Configuration: $1s^2\,2s^2$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 0$, $m_l = 0$, $m_s = -\frac{1}{2}$
  • 15. Boron (Boro):
    • Chemical Symbol: $\text{B}$
    • Electron Configuration: $1s^2\,2s^2\,2p^1$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 1$, $m_l = -1$, $m_s = +\frac{1}{2}$
  • 16. Carbon (Carbono):
    • Chemical Symbol: $\text{C}$
    • Electron Configuration: $1s^2\,2s^2\,2p^2$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 1$, $m_l = 0$, $m_s = +\frac{1}{2}$
  • 17. Nitrogen (Nitrógeno):
    • Chemical Symbol: $\text{N}$
    • Electron Configuration: $1s^2\,2s^2\,2p^3$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 1$, $m_l = +1$, $m_s = +\frac{1}{2}$
  • 18. Oxygen (Oxígeno):
    • Chemical Symbol: $\text{O}$
    • Electron Configuration: $1s^2\,2s^2\,2p^4$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 1$, $m_l = -1$, $m_s = -\frac{1}{2}$
  • 19. Fluorine (Flúor):
    • Chemical Symbol: $\text{F}$
    • Electron Configuration: $1s^2\,2s^2\,2p^5$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 1$, $m_l = 0$, $m_s = -\frac{1}{2}$
  • 20. Neon (Neón):
    • Chemical Symbol: $\text{Ne}$
    • Electron Configuration: $1s^2\,2s^2\,2p^6$
    • Differentiating Electron Quantum Set: $n = 2$, $l = 1$, $m_l = +1$, $m_s = -\frac{1}{2}$

Valence Electrons and Periodic Trends of Elements 21 Through 30

• Valence Electron Concept and Chemical Reactivity:

  • Valence electrons are defined as the electrons situated in the highest principal energy level (outermost electron shell) of an atom.
  • The total number of valence electrons determines an element's chemical properties, valence capability, Lewis dot diagram structure, and primary bonding behaviors.

• Elemental Inventory and Outer-Shell Characteristics (Catalog Series 21 to 30):

  • 21. Sodium (Sodio):
    • Chemical Symbol: $\text{Na}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^1$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^1$
    • Number of Valence Electrons: $1$
    • Periodic Group: Group 1 (Alkali metals)
  • 22. Magnesium (Magnesio):
    • Chemical Symbol: $\text{Mg}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2$
    • Number of Valence Electrons: $2$
    • Periodic Group: Group 2 (Alkaline earth metals)
  • 23. Aluminum (Aluminio):
    • Chemical Symbol: $\text{Al}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^1$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2\,3p^1$
    • Number of Valence Electrons: $3$
    • Periodic Group: Group 13 (Boron group / post-transition metals)
  • 24. Silicon (Silicio):
    • Chemical Symbol: $\text{Si}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^2$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2\,3p^2$
    • Number of Valence Electrons: $4$
    • Periodic Group: Group 14 (Carbon group / metalloids)
  • 25. Phosphorus (Fósforo):
    • Chemical Symbol: $\text{P}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^3$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2\,3p^3$
    • Number of Valence Electrons: $5$
    • Periodic Group: Group 15 (Pnictogens / nonmetals)
  • 26. Sulfur (Azufre):
    • Chemical Symbol: $\text{S}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^4$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2\,3p^4$
    • Number of Valence Electrons: $6$
    • Periodic Group: Group 16 (Chalcogens / reactive nonmetals)
  • 27. Chlorine (Cloro):
    • Chemical Symbol: $\text{Cl}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^5$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2\,3p^5$
    • Number of Valence Electrons: $7$
    • Periodic Group: Group 17 (Halogens)
  • 28. Argon (Argón):
    • Chemical Symbol: $\text{Ar}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$
    • Condensed Noble Gas Configuration: $[\text{Ne}]\,3s^2\,3p^6$
    • Number of Valence Electrons: $8$
    • Periodic Group: Group 18 (Noble gases; complete, stable octet)
  • 29. Potassium (Potasio):
    • Chemical Symbol: $\text{K}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^1$
    • Condensed Noble Gas Configuration: $[\text{Ar}]\,4s^1$
    • Number of Valence Electrons: $1$
    • Periodic Group: Group 1 (Alkali metals, Period 4)
  • 30. Calcium (Calcio):
    • Chemical Symbol: $\text{Ca}$
    • Complete Ground-State Electron Configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2$
    • Condensed Noble Gas Configuration: $[\text{Ar}]\,4s^2$
    • Number of Valence Electrons: $2$
    • Periodic Group: Group 2 (Alkaline earth metals, Period 4)