Study sheet: Quantum Model and Periodic Classification

📋 Course Outline

1. Atomic Structure and Elementary Particles
2. Electron Discovery and Classical Model
3. Electromagnetic Radiation and Spectra
4. Quantized Energy Levels
5. Schrödinger Equation and Orbitals
6. Quantum Numbers and Orbital Shapes
7. Electronic Configuration Rules
8. Valence Electrons and Ions
9. Periodic Table Organization
10. Periodic Properties and Electronegativity

📅 Key Dates

1. 1869Mendeleïev organized known elements by increasing atomic mass and grouped elements with similar properties, leaving gaps for undiscovered elements
2. 1900the electron was discovered with charge −e = −1.6 × 10⁻¹⁹ C and mass 9.1095 × 10⁻³¹ kg, much smaller than the mass of nucleons
3. 1925Erwin Schrödinger established the Schrödinger equation to describe the time evolution of a particle probabilistically

📖 1. Atomic Structure and Elementary Particles

🔑 Key Concepts & Definitions

• Atom : consists of one atomic nucleus and electrons surrounding it

★ Must-know

• The electron has a charge of −1.6 × 10⁻¹⁹ C and a mass of 9.1 × 10⁻³¹ kg.

Further detail

📌 Leptons, including electrons and mesons in the course classification, have low mass, whereas baryons, including protons and neutrons, have greater mass.

• Each particle is associated with an antiparticle, such as the electron with the positron and the proton with the antiproton.

💡 Memory Hook

Leptons are light; baryons are heavier.

📖 2. Electron Discovery and Classical Model

📝 Essential Points

• In the classical model, an orbiting electron is subjected to centrifugal force and electrostatic attraction to the positively charged nucleus.

📌 If the atom continuously lost electromagnetic energy, the electron would fall onto the nucleus and the atom would emit a continuous spectrum.

💡 Memory Hook

Continuous energy loss → electron collapse and continuous emission.

📖 3. Electromagnetic Radiation and Spectra

🔑 Key Concepts & Definitions

• Frequency : the periodic oscillation rate of electromagnetic fields, measured in hertz

★ Must-know

📐 Formula — The wavelength of electromagnetic radiation satisfies $\lambda = \frac{c}{\nu}$, where c is the speed of light and ν is frequency.

📐 Formula — The energy of electromagnetic radiation satisfies $E = h\nu = \frac{hc}{\lambda}$, with c = 3 × 10⁸ m/s and h = 6.6262 × 10⁻³⁴ J·s.

• An excited atom emits only certain frequencies characteristic of the element, producing a discontinuous line spectrum.

Further detail

📌 An electromagnetic wave has an ondulatory nature through its wavelength and a corpuscular nature through photons, each photon having energy E = hν.

💡 Memory Hook

Continuous spectrum versus characteristic line spectrum.

📖 4. Quantized Energy Levels

🔑 Key Concepts & Definitions

• Quantized energy levels : discrete allowed values of an atom’s internal energy

★ Must-know

📐 Formula — For an electronic transition, the energy difference satisfies $\Delta E = E_{initial} - E_{final} = \frac{hc}{\lambda}$.

📌 Absorption and emission are complementary processes caused by electrons moving between distinct energy levels.

Further detail

• Measuring emitted or absorbed radiation makes it possible to determine the electronic energy levels of an atom.

💡 Memory Hook

Energy-level transitions → absorption or emission of photons.

📖 5. Schrödinger Equation and Orbitals

🔑 Key Concepts & Definitions

• Atomic orbital : a solution of the Schrödinger equation that describes an electron’s energy and probability of presence in space

★ Must-know

• An orbital is represented by a region in which there is a 99% chance of finding the electron or electrons associated with it.

Further detail

• The Schrödinger equation can calculate the energy levels of hydrogen, which contains one proton and one electron, although its formal solution is not part of the first-year program.

💡 Memory Hook

An electron cloud surrounds the nucleus rather than following a fixed path.

📖 6. Quantum Numbers and Orbital Shapes

🔑 Key Concepts & Definitions

• Principal quantum number : a positive integer starting at 1 that defines the principal energy level and shell, with a maximum capacity of 2n² electrons

★ Must-know

📌 The azimuthal quantum number l satisfies $0 \le l \le n-1$ and defines the subshell and orbital geometry.

📌 The magnetic quantum number m satisfies $-l \le m \le l$ and defines the orientation of the orbital angular momentum.

• The spin quantum number s has the two values +1/2 and −1/2 and describes the orientation of the electron’s intrinsic magnetic moment.

Further detail

• The orbital labels corresponding to l = 0, 1, 2, 3, and 4 are respectively s, p, d, f, and g.

• The hydrogen ground-state electron occupies the 1s orbital with n = 1, l = 0, and m = 0.

💡 Memory Hook

n defines the shell, l the subshell, m the orientation, and s the spin.

📖 7. Electronic Configuration Rules

★ Must-know

• The Pauli exclusion principle states that two electrons in the same atom cannot have identical values of all four quantum numbers.

• The Klechkowski rule fills orbitals in increasing order of n + l, and for equal n + l it fills the orbital with lower n first.

• Hund’s rule states that orbitals with the same l are first occupied by one electron each before any receives a second electron of opposite spin.

• A subshell with angular quantum number l contains 2l + 1 orbitals, and each orbital can contain at most two electrons.

Further detail

• The ground-state electronic configuration of carbon with Z = 6 is 1s² 2s² 2p², with the two 2p electrons occupying separate p orbitals.

💡 Memory Hook

Pauli limits occupancy, Klechkowski orders energy, Hund fills singly first.

📖 8. Valence Electrons and Ions

🔑 Key Concepts & Definitions

• Valence shell : the set of outer electronic orbitals whose electrons mainly determine the chemical properties of atoms, ions, and molecules

★ Must-know

📌 Atoms generally gain or lose electrons to approach the stable electronic configuration of the nearest noble gas.

📌 For cations, electrons are removed first from orbitals with the highest principal quantum number n.

Further detail

• Lithium has configuration 1s² 2s¹ and readily forms Li⁺ with configuration 1s², matching helium.

• Chlorine has configuration [Ne] 3s² 3p⁵ and readily forms Cl⁻ with configuration [Ne] 3s² 3p⁶, matching argon.

• The noble gases cited are:

  • helium
  • neon
  • argon
  • krypton

• The cited exceptional configurations are:

  • chromium [Ar] 4s¹ 3d⁵
  • copper [Ar] 4s¹ 3d¹⁰
  • palladium [Kr] 4d¹⁰

💡 Memory Hook

Valence configuration → chemical reactivity and noble-gas-like ions.

📖 9. Periodic Table Organization

📝 Essential Points

• The modern periodic table has seven periods, and elements in the same period have the same principal quantum number n.

• The periodic table contains 18 columns grouped into the s, p, d, and f blocks containing respectively 2, 6, 10, and 14 columns.

📌 Elements in the same group have analogous chemical properties because they have similar external electronic configurations.

• The cited family configurations are:
  • alkali metals: ns¹
  • alkaline-earth metals: ns²
  • halogens: ns²np⁵
  • noble gases: ns²np⁶

💡 Memory Hook

Periods share n; groups share external configurations and properties.

📖 10. Periodic Properties and Electronegativity

🔑 Key Concepts & Definitions

• Ionization energy : the energy required to remove one electron from a neutral atom
• Electronegativity : an atom’s ability to attract or lose electrons; in Mulliken’s definition, $X = \frac{E_i + A}{2}$
• Electron affinity : the energy released when an atom accepts an electron, represented by A + e⁻ → A⁻ + A

★ Must-know

📌 Atomic radius generally decreases from left to right across a period and increases from top to bottom within a group.

📌 First ionization energy generally increases across a period and decreases down a group.

• In NaCl formation, sodium transfers its 3s electron to highly electronegative chlorine, producing Na⁺ with [Ne] and Cl⁻ with [Ar].

Further detail

• Fluorine is the most electronegative element, with an electronegativity close to 4 in the cited scale.

💡 Memory Hook

Atomic radius increases down a group, whereas ionization energy generally decreases.

📊 Synthesis Tables

Quantum Numbers

Number	Allowed values	Main role
n	1, 2, 3, …	Principal shell and energy level
l	0 to n − 1	Subshell and orbital geometry
m	−l to +l	Orbital orientation
s	+1/2 or −1/2	Electron spin orientation