UNIT 2: Quantum Theory and Electronic Structure PDF

**UNIT 2: QUANTUM THEORY AND ELECTRONIC STRUCTURE** **The Development of Atomic Theory:** Atomic Theory Timeline +-----------------------------------+-----------------------------------+ | **Democritus** | **Atomos** | |...

**UNIT 2: QUANTUM THEORY AND ELECTRONIC STRUCTURE** **The Development of Atomic Theory:** Atomic Theory Timeline +-----------------------------------+-----------------------------------+ | **Democritus** | **Atomos** | | | | | **(600 BC)** | All things are composed of the | | | atomos or the fundamental | | | particles, atoms. | +===================================+===================================+ | **John Dalton** | **Solid Sphere** | | | | | **(1803)** | All objects are made of particles | | | called atoms and that they are | | | solid spheres that cannot be | | | divided further into smaller | | | particles. | +-----------------------------------+-----------------------------------+ | **J. J. Thomson** | **Plum Pudding** | | | | | **(1897)** | Thomson proposed in 1897 that the | | | basic body of an atom is | | | spherical in shape, with | | | electrons (small particles within | | | the atom that have a negative | | | charge) and a positively charged | | | "jelly" surrounding the electrons | | | that neutralizes the charge of | | | the electrons. | +-----------------------------------+-----------------------------------+ | **Ernest Rutherford (1911)** | **Nuclear** | | | | | | An atom is mostly empty space, | | | with electrons orbiting a fixed, | | | positively charged nucleus in | | | set, predictable paths | +-----------------------------------+-----------------------------------+ | **Niels Bohr (1913)** | **Planetary** | | | | | | The electrons travel around the | | | nucleus of an atom in distinct | | | circular orbits, or shells. | +-----------------------------------+-----------------------------------+ | **Erwin Schrödinger (1926)** | **Quantum-wave** | | | | | | Electrons are undulations of | | | matter, that is, it describes the | | | wave behavior of the electron. | +-----------------------------------+-----------------------------------+ | **James Chadwick** | **Neutrons** | | | | | **(1932)** | Proved the existence of neutrons | | | -- elementary particles devoid of | | | any electrical charge. | +-----------------------------------+-----------------------------------+ **Dalton's Atomic Theory** *(Solid sphere)* **THE DEVELOPMENT OF ATOMIC THEORY: John Dalton (1803)** 1. **Law of Constant Composition/Law of Definite proportion** (Postulates 4) - in a given compound, the relative numbers and kinds of atoms are constant. - (ex. H~2~ + O = H~2~O) 2. **Law of Conservation of Mass** (Postulates 3) - the total mass of materials present after a chemical reaction is the same as the total mass present before the reaction. - (ex. X \[1 g\] + Y \[0.333 g\] = XY \[1.333 g\]) 3. **Law of Multiple Proportions** - if two elements A and B combine to form more than one compound, the masses of B that can combine with a given mass of A are in the same ratio of small whole numbers. - (ex. CO \[1.333 g\] + O \[0.333 g\] = CO \[1.333 g\]) **THE DEVELOPMENT OF ATOMIC THEORY: J.J. Thomson (1897)** **Cathode Rays -- composed of negatively charged particles called "electrons".** **Cathode Ray Tube Experiment** --electrons are accelerated from one end of the tube to the other using an electric field - led to the discovery of electrons. - Plum pudding model **THE DEVELOPMENT OF ATOMIC THEORY: Ernest Rutherford (1911)** **α Scattering Experiment** - directed high energy streams of α-particles from a radioactive source at a thin sheet (100 nm thickness) of gold. - most of the mass of each gold atom and all of its positive charge reside in a very small, extremely dense region called **nucleus**. - most of the volume of an atom is an empty space. - most of the particles passed through the foil unscattered. - Repulsion between the highly positive charge of the gold nucleus and the positive charge of the alpha particle caused it to deflect. **Nuclear Model of an Atom** - much of an atom's positive charge is concentrated in a relatively tiny volume at the center of the atom, known as the **nucleus**, where positively charged particles called **protons** reside. - Atom itself is about 100,000 (10^5^) times the diameter of the nucleus. **THE DEVELOPMENT OF ATOMIC THEORY: James Chadwick (1932)** - Discovered the neutral particles called **neutrons** - Nucleus contains two types of particles: Protons (positively charged) Neutrons (neutral). +-----------------------------------------------------------------------+ | **DISCOVERIES:** | +=======================================================================+ | - **John Dalton** -- (3) Atomic Laws | +-----------------------------------------------------------------------+ | - **J.J. Thomson** -- Electron (through Cathode Ray Tube | | Experiment) | +-----------------------------------------------------------------------+ | - **Ernest Rutherford** -- Protons (through **α** Scattering | | Experiment) | +-----------------------------------------------------------------------+ **TODAY'S ATOMIC MODEL:** - composed of protons, neutrons, and electrons - dense positively charged nucleus - negatively charged electron cloud - mostly empty space **SUBATOMIC PARTICLES:** Particle Symbol Loc Relative electric charge Mass (amu) Actual mass, g ---------- -------- -------------------------- -------------------------- ---------------- ---------------- Electron e^-^ Space around the nucleus 1- 5.486 x 10^-4^ 9.11 x 10^-28^ Proton p^+^ Nucleus 1+ 1.0073 1.67 x 10^-24^ Neutron n^0^ Nucleus 0 1.0087 1.68 x 10^-24^ **1 amu = 1.66054 x 10^-24^ g** - every atom has an **equal number** of electrons and protons (no net electrical charge) - most of the mass of the atom is in the nucleus. (protons + neutrons = **nucleons**) - Electrons are found outside the nucleus (**electron cloud**) - most of the volume of an atom is an **empty space** **ATOMIC NUMBER, MASS NUMBER AND ISOTOPES** +-----------------------------------+-----------------------------------+ | **^M^X ~N~X** | **X** -- atomic symbol | | | | | | \- symbol of element | +===================================+===================================+ | | **M** -- atomic mass | | | | | | \- mass of protons and neutrons | +-----------------------------------+-----------------------------------+ | | **N** -- atomic number | | | | | | \- number of protons | +-----------------------------------+-----------------------------------+ | **p^+^ = e^-^ :** the number of | | | protons is equal to the number of | | | electrons | | +-----------------------------------+-----------------------------------+ ***Isotopes*** - atoms of the [same element] (same number of **protons**) but [different number] of **neutrons** in their nuclei. - Atoms with the same atomic number but different atomic mass. ------------------------------------------------------------------------------------------------------------------------------- \ \ \ [~6~^12^*C*]{.math.display}\ [~6~^13^*C*]{.math.display}\ [~6~^14^*C*]{.math.display}\ ------------------------------- ------------------------------- ------------------------------- ------------------------------- \ \ \ [~6~^12^*C*]{.math.display}\ [~6~^13^*C*]{.math.display}\ [~6~^14^*C*]{.math.display}\ **A** 12 13 14 **p^+^** 6 6 6 **e^-^** 6 6 6 **n^0^** 6 7 8 ------------------------------------------------------------------------------------------------------------------------------- **ACCOUNTING OF SUB-ATOMIC PARTICLES FOR IONS** +-------------+-------------+-------------+-------------+-------------+ | Ion | Number of | | | | | | Particles | | | | +=============+=============+=============+=============+=============+ | | Electrons | Protons = Z | Nucleons | Neutrons = | | | | | (protons + | N = (A-Z) | | | | | neutrons) = | | | | | | A | | +-------------+-------------+-------------+-------------+-------------+ | **Atom:** | 11 | 11 | 23 | 12 | | | | | | | | \ | | | | | | [~11~^23^Na | | | | | | ]{.math | | | | | |.display}\ | | | | | +-------------+-------------+-------------+-------------+-------------+ | **Cation:** | 11-1=10 | | | | | | | | | | | Na^+^ (less | | | | | | 1 electron) | | | | | +-------------+-------------+-------------+-------------+-------------+ | **Atom:** | 9 | 9 | 19 | 10 | | | | | | | | \ | | | | | | [~9~^19^Fe] | | | | | | {.math | | | | | |.display}\ | | | | | +-------------+-------------+-------------+-------------+-------------+ | **Anion:** | 9+1=10 | | | | | | | | | | | Fe^-^ (add | | | | | | one | | | | | | electron) | | | | | +-------------+-------------+-------------+-------------+-------------+ **Mass of Individual Atoms** - Atomic mass of an element is the weighted average mass of isotopes of that element. \ [(atomic mass of element x percentage) + (atomic mass of isotope x percentage) = *average* *mass*/*atomic* *mass*]{.math.display}\ **Rejection of Rutherford's** **Atomic Model:** - Atoms are stable in nature *(not with Rutherford's that states it becomes unstable due to the falling of e^-^ towards the nucleus)* - Bohr infer that electron orbit the nucleus similar with how the planets rotates around the sun. Rising the idea of **Planetary Atomic Model**. **Bohr's model -- Planetary Model** (Neils Bohr, 1913) - The electron of the atom can exist only in certain circular orbits around the nucleus in certain specific radii. **Bohr's (3) Postulates:** 1. The electrons revolve around the nucleus in a fixed orbit. 2. They do not deviate from their path. 3. The electrons can make a jump from one orbit to another one. (With proton energy E = hv) **Ground State** -- lowest energy state of an; most stable. **Excited State** -- higher energy state **QUANTUM** a **quantum staircase** as an analogy for atomic energy levels. - **"n"** represents energy levels (n = 1,2,3,4...) - Higher **n** value means higher energy level. - **"Energy is quantized"** when an electron [falls back to the lower level/jumps to the higher level] it **emits/absorbs** a definite amount of energy in the form of quantum of light. - [\$\\mathbf{E =}\\frac{\\text{hc}}{\\lambda}\$]{.math.inline} - λ = lambda **ERWIN SCHRÖDINGER'S QUANTUM MECHANICAL MODEL OF AN ATOM** **Bohr vs. Electron Cloud** - regions around the nucleus of an atom where an electron is likely to be found. - clouds showing the region of probable electron locations. **Electron density (density of the electron cloud)** - Region of high e^-^ density = high probability of finding an e^-^. - Region of low e^-^ density -- low probability of finding an e^-^. - **Heisenberg's Uncertainty Principle** - states that it is not possible to measure precisely both the **velocity** (momentum) and the **position** of an electron at the same time. - **Louis de Broglie** - proposed that electrons might also have wave-particle nature *(electrons have wave properties).* - Devised an equation that treated electrons as waves. - **Ψ** -- wave function, describe the electron of an atom and (**Ψ^2^**) provides info about its location. - Location cannot be described, (**Ψ^2^**) represents the probability that the electron can be found at a certain region**.** - (**Ψ^2^**) -- **probability density** or **electron density**. - Wave functions = foundation of wave theory. - **Quantum Theory** -- describe mathematically the wave properties of the electrons. - **Orbitals** -- a set of wave functions. **QUANTUM NUMBERS AND ATOMIC ORBITALS** - **Quantum numbers** -- are dimensionless numbers which completely describe the **state of an electron**. - Four quantum numbers describe the distribution and behavior of electrons in atoms. - Each wave function, Ψ, corresponds to a set of three quantum numbers and is referred to as an **atomic orbital** (has characteristic shape and energy). +-----------------------------------------------------------------------+ | **(4) QUANTUM NUMBERS:** | +=======================================================================+ | 1. **Principal quantum number \[n\]** | | | | - describes the **distance between the nucleus and the shell**. | | | | - as n increase, on average, the electron is found farther out of | | the nucleus. | | | | - describes the level of the shell -- as **"n"** increases, the | | energy of the electron increases and is therefore less tightly | | bound to the nucleus. | | | | - can have an integral value **1,2,3,4.... Etc.** | | | | - numbers of electrons that can be accommodated in a given shell is | | equal to **\[2n^2^\]**. | | | |  | +-----------------------------------------------------------------------+ | 2. **Azimuthal/ Angular Momentum Quantum Number, \[l\]** | | | | - defines the shape of the orbital | | | | - describes the energy level of the subshells | | | | - number of subshells in a shell is equal to n | | | | - has any integral value starting from 0 to (n-1) | | | | *Table 1. Azimuthal quantum number* | | | | l values Symbol No. of orbitals Shape | | ---------- -------- ----------------- ------------ | | 0 s 1 spherical | | 1 p 3 dumbbell | | 2 d 5 four-lobe | | 3 f 7 eight-lobe | | | | - each subshell consists of a set of orbitals | | | | - all the orbitals in the same subshell have the same energy | | | | - within a given shell, the energies of the electrons in the | | orbitals increase in the following order: \< np \< nd \< nf. | | | | **Principal Quantum Number Symbol:** | | | | Angular Momentum Quantum Number Symbol: | | | | +---------------------+---------------------+---------------------+ | | | Principal Quantum | Angular Momentum | Subshells | | | | No. \[n\] | Quantum No. \[l\] | | | | +=====================+=====================+=====================+ | | | 1 | l = 0 | s | | | | | | | | | | | | (1 subshell) | | | +---------------------+---------------------+---------------------+ | | | 2 | l = 0,1 | s, p | | | | | | | | | | | | (2 subshells) | | | +---------------------+---------------------+---------------------+ | | | 3 | l = 0,1,2 | s, p, d | | | | | | | | | | | | (3 subshells) | | | +---------------------+---------------------+---------------------+ | | | 4 | l = 0,1,2,3 | s, p, d, f | | | | | | | | | | | | (4 subshells) | | | +---------------------+---------------------+---------------------+ | +-----------------------------------------------------------------------+ | 3. **Magnetic Quantum Number \[m~l~\]** | | | | - describes the orientation of the atomic orbitals in space. | | | | - distinguishes orbitals within a given sub-shell that have | | different shapes and orientation in space | | | | - each subshell is divided into **"orbitals"**, each capable of | | holding a pair of electrons | | | | - can have any integer value from \[-\] to \[+\] | | | | - each orbital within a given subshell has the same energy. | | | |  | +-----------------------------------------------------------------------+ | 4. **Spin Quantum Number \[m~s~\]** | | | | - describes the direction of spin of an electron about its own | | axis: counterclockwise, **m~s~ = -** **½,** clockwise, **m~s~ = | | ½**. | | | | - Electrons with the **same spin quantum | | numbers** have [parallel spins] while those with | | **different m~s~ values** have [opposite spin.] | +-----------------------------------------------------------------------+ *Table 8.1 Summary of Quantum Numbers of Electrons in Atoms* +-----------------+-----------------+-----------------+-----------------+ | **Name** | **Symbol** | **Permitted | **Property** | | | | Values** | | +=================+=================+=================+=================+ | Principal | n | 1, 2, 3, 4... | Distance of | | | | | nucleus and | | | | Positive | shell | | | | integers | | +-----------------+-----------------+-----------------+-----------------+ | Azimuthal/ | l | 0,1,2,3 | Shape of | | Angular | | | orbitals | | Momentum | | 0 to n-1 | | +-----------------+-----------------+-----------------+-----------------+ | Magnetic | m~l~ | (-) to (+) | Orientation of | | | | | orbitals in | | | | Integers from - | space | | | | 0 + | | +-----------------+-----------------+-----------------+-----------------+ | Spin | m~s~ | ± ½ | Rotation of | | | | | orbital | | | | | (direction of | | | | | e^-^ spin) | +-----------------+-----------------+-----------------+-----------------+