Atomic Theory, Nuclear Structure, Mole Conversions, and Light Properties Flashcards

Historical Development of the Atomic Theory

• Democritus ($400\,\text{BC}$):

  • A Greek philosopher who introduced the term "atom", which translates to "invisible".

  • Proposed the foundational concept of the indivisible atom.

• John Dalton ($1800\text{s}$):

  • Discovered that all matter consists of tiny, indivisible particles called atoms.

  • Stated that atoms are indestructible and unchangeable.

  • Established that elements are characterized by the weight of their atoms, and that the atoms of every distinct element possess a different weight.

  • Demonstrated that atoms combine to form new chemical compounds.

  • Proposed the Unchangeable Elements / Solid Sphere atomic model.

• J. J. Thomson ($1890\text{s}$):

  • A physicist who discovered the electron using cathode ray tube technology.

  • Discovered the electron and characterized its negative charge.

  • Proposed the Plum Pudding Model, which depicts negatively charged corpuscles (electrons) embedded within a positively charged fluid sphere.

• Ernest Rutherford ($1900\text{s}$):

  • Discovered the dense atomic nucleus and determined that electrons orbit around this nucleus.

  • Proposed the Planetary / Atomic Model featuring a central positively charged nucleus.

• Niels Bohr ($1910\text{s}$):

  • Discovered that electrons orbit the nucleus in specific circular orbits that possess fixed sizes and energy levels.

  • Agreed with and refined the planetary atomic model.

• Erwin Schrödinger ($1920\text{s}$):

  • A revolutionary physicist who developed the quantum mechanical atomic model used today.

  • Developed the modern Atomic Model consisting of a central positively charged nucleus containing protons ($p^+$) and neutrons ($n^0$), surrounded by electrons in designated energy levels.

  • Established that every single electron possesses its own unique "identity", which is precisely specified by a set of Quantum Numbers ($\text{Quantum \#s}$).

Fundamental Forces of Nature

• The Four Fundamental Forces:

  • Nuclear Force (Strong Nuclear Force):

  • An attractive force acting between pairs of subatomic particles: proton-neutron ($p^+-n^0$), proton-proton ($p^+-p^+$), and neutron-neutron ($n^0-n^0$).

  • Operates over an extremely short range of $1\,\text{fm} = 1 \times 10^{-15}\,\text{m}$ (also noted as $1 \times 10^{-24}\,\text{m}$ on extended subatomic scales).

  • Electromagnetic Forces:

  • Forces exerted between charged particles, involving attraction between opposite charges ($+$ and $-$) and repulsion between like charges ($+$ and $+$, or $-$ and $-$).

  • Weak Nuclear Forces:

  • Short-range interactions responsible for particle breakdown and radioactive decay processes.

  • Gravitational Pull (Gravity):

  • An attractive force exerted between objects purely due to their mass.

Atomic Structure, Mass, and Isotope Notation

• Atomic Number ($Z$):

  • Defined as the total number of protons ($p^+$) present in the nucleus of each atom of a specific element.

• Isotopes:

  • Atoms belonging to the same element that possess identical atomic numbers (protons) but different mass numbers due to varying quantities of neutrons.

• Mass Number ($A$):

  • The combined total count of protons and neutrons in an atomic nucleus:     $\text{Mass Number} = p^+ + n^0$

• Hyphen Notation:

  • Formatted as the element name followed by a hyphen and its mass number, such as $\text{Uranium-235}$.

  • Example calculation for $\text{Uranium-235}$:

  • Mass Number ($A$): $235$

  • Atomic Number / Protons ($p^+$ ): $92$

  • Calculation of Neutrons ($n^0$):       $n^0 = 235 - 92 = 143$

• Nuclear Symbol Notation:

  • Formatted as ${^{A}_{Z}\text{X}}$, where the superscript indicates the mass number ($A$) and the subscript indicates the atomic number ($Z$).

  • Symbol for Uranium-235:     ${^{235}_{92}\text{U}}$

  • cThe superscript $235$ represents the mass number, and the subscript $92$ represents the atomic number.

• Atomic Mass Unit ($\text{amu}$):

  • One atomic mass unit ($1\,\text{amu}$) is defined as exactly $\frac{1}{12}$ the mass of a single carbon-12 ($^{12}\text{C}$) atom.

  • The atomic mass of any element is experimentally measured relative to this carbon-12 standard.

• Average Atomic Mass:

  • The weighted average mass of all naturally occurring isotopes of an element based on their relative natural abundance.

The Mole Concept and Avogadro's Number

• The Mole:

  • The standard SI unit used to quantify the amount of substance.

  • One mole ($1\,\text{mol}$) of any substance contains exactly $6.022 \times 10^{23}$ representative particles.

• Avogadro's Number:

  • Defined as $6.022 \times 10^{23}$.

  • Represents the count of fundamental entities in one mole, which can consist of:

  • Atoms

  • Molecules

  • Electrons

  • Ions

Mole Conversion Relationships

• Dimensional Analysis and Conversion Operations:

  • Mass (grams) to Amount (moles):

  • Divide the mass in grams by the molar mass (grams per mole):       $\text{moles} = \text{grams} \times \frac{1\,\text{mol}}{\text{molar mass (grams)}}$

  • Amount (moles) to Mass (grams):

  • Multiply the amount in moles by the molar mass:       $\text{grams} = \text{moles} \times \frac{\text{molar mass (grams)}}{1\,\text{mole}}$

  • Amount (moles) to Particles (atoms or molecules):

  • Multiply the amount in moles by Avogadro's number ($6.022 \times 10^{23}$):       $\text{particles} = \text{moles} \times \frac{6.022 \times 10^{23}\,\text{particles}}{1\,\text{mole}}$

  • Particles (atoms or molecules) to Amount (moles):

  • Divide the particle count by Avogadro's number ($6.022 \times 10^{23}$):       $\text{moles} = \text{particles} \times \frac{1\,\text{mole}}{6.022 \times 10^{23}\,\text{particles}}$

Properties of Light and Quantum Concepts

• Electromagnetic Radiation:

  • A form of energy that exhibits wavelike behavior while traveling through space.

• Electromagnetic Spectrum:

  • The complete continuum containing all existing forms of electromagnetic radiation.

• Wavelength ($\lambda$):

  • The physical distance separating corresponding points on adjacent waves (e.g., crest to crest or trough to trough).

• Frequency ($\nu$):

  • The total number of complete wave cycles that pass a given point in a specified amount of time, typically measured per second ($\text{s}^{-1}$ or $\text{Hz}$).

• Period:

  • The exact duration of time required to complete one full wave period or cycle.

• Photoelectric Effect:

  • The phenomenon in which electrons are ejected from the surface of a metal when light shines upon that metal.

• Quantum of Energy:

  • The minimum quantity of energy that can be absorbed or released by an atom.

Quantum Mechanics and Electron Configurations

• Quantum Theory:

  • describes mathematically the wave properties of electrons and other very small particles.

• Energy States of Atoms:

  • Ground State:

  • The lowest potential energy state of an atom, where all electrons occupy the lowest available energy levels.

  • Excited State:

  • A state possessing higher potential energy than the ground state, occurring when an electron absorbs energy and moves to a higher energy level.

• Photon Dynamics:

  • Photon:

  • a particle of electromagnetic radiation having zero mass and carrying a quantum of energy.

  • Absorption:

  • The process by which an atom absorbs electromagnetic energy, causing an electron to move to a higher energy level.

  • Emission:

  • The release of energy as a photon when an electron falls from a higher energy level to a lower energy level.

• Atomic Orbitals and Quantum Numbers:

  • Orbital:

  • A three-dimensional mathematical region around the nucleus where there is a high probability ($90\%$ or greater) of finding an electron.

  • Quantum Numbers:

  • A set of four values ($n$, $l$, $m_l$, $m_s$ ) that uniquely define the energy level, orbital shape, spatial orientation, and spin state of an electron.

• Electron Arrangement and Configuration Rules:

  • Electron Configuration:

  • The specific arrangement and distribution of electrons within an atom's orbitals.

  • Orbital Notation:

  • A visual representation of electron configurations using boxes or lines for orbitals and arrows for electron spins.

  • Aufbau Principle:

  • States that electrons occupy the lowest-energy orbitals available before occupying higher-energy orbitals.

  • Pauli Exclusion Principle:

  • States that no two electrons in an atom can have the exact same set of four quantum numbers; an orbital can hold at most two electrons with opposite spins.

  • Hund's Rule:

  • States that orbitals of equal energy are each occupied by one electron with parallel spin before any orbital receives a second electron.

The 4 Quantum Numbers

1. Principal Quantum Number ($n$) - Energy Level / Size

   • What it represents: The main energy level or electron shell.

   • In simple terms: It tells you how far away from the nucleus the electron mostly lives. Larger $n$ values mean higher energy and a larger orbital ($n = 1, 2, 3, \dots$).

2. Angular Momentum Quantum Number ($l$) - Shape of Sublevel

   • What it represents: The shape of the electron orbital.

   • In simple terms: It tells you the type/shape of the region where the electron moves ($s$, $p$, $d$, or $f$).

3. Magnetic Quantum Number ($m_l$ ) - Orientation in Space

   • What it represents: The 3D direction of an orbital.

   • In simple terms: If an orbital shape has multiple ways it can point in space (like along the x, y, or z axis), $m_l$ specifies which way it points.

4. Spin Quantum Number ($m_s$) - Electron Spin

   • What it represents: The spin direction of the electron.

   • In simple terms: Electrons act like tiny spinning tops. They can spin either spin-up ($+\frac{1}{2}$) or spin-down ($-\frac{1}{2}$).

The Sublevels: $s$, $p$, $d$, and $f$

These letters represent the different orbital shapes and electron capacities:

• Sublevel $s$:

  • Shape: Spherical (ball-shaped).

  • Orbitals: $1$ orbital.

  • Maximum Capacity: Holds up to $2$ electrons.

• Sublevel $p$:

  • Shape: Dumbbell-shaped.

  • Orbitals: $3$ orbitals.

  • Maximum Capacity: Holds up to $6$ electrons ($2$ per orbital).

• Sublevel $d$:

  • Shape: Cloverleaf-shaped (more complex).

  • Orbitals: $5$ orbitals.

  • Maximum Capacity: Holds up to $10$ electrons.

• Sublevel $f$:

  • Shape: Complex multi-lobed shape.

  • Orbitals: $7$ orbitals.

  • Maximum Capacity: Holds up to $14$ electrons.