CHEM 101 Part 3 2021-2022 Lecture Notes PDF

(Lec. 05) Inorganic Chemistry Group 2021-2022  Outlines Quantum mechanical model of the atom. Schrödinger's equation. Wave Function of Hydrogen Atom. Quantum Numbers. Shapes of orbitals. Inorganic Chemistry Group 2021-2...

(Lec. 05) Inorganic Chemistry Group 2021-2022  Outlines Quantum mechanical model of the atom. Schrödinger's equation. Wave Function of Hydrogen Atom. Quantum Numbers. Shapes of orbitals. Inorganic Chemistry Group 2021-2022 Quantum mechanical model atom (Where is the electron located?) Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves. Inorganic Chemistry Group 2021-2022 Schrödinger equation (Schrödinger wave equation) A partial differential equation describing the propagation of the wave associated with the particle. ‫معادلة تفاضلية جزئية تصف انتشار الموجة المرتبطة بالجسيم‬ Inorganic Chemistry Group 2021-2022 Schrödinger equation (Schrödinger wave equation) Hψ =Eψ H: Hamiltonian operator (K.E + P.E) for the electron. E: Eigenfunction (Express the Energy levels That can The electron occupy). ψ : Wave Function (A function that describes the waveform of the probability distribution of an electron's location( Inorganic Chemistry Group 2021-2022  Schrödinger equation (Schrödinger wave equation) Wave Equation H ψ = E ψ Wave function (Solution of Wave equation) (ψ ) Probability of finding electron in a space (ψ2) Inorganic Chemistry Group 2021-2022 Wave Function of Hydrogen Atom z r cos θ electron θ r y φ x Inorganic Chemistry Group 2021-2022 Schrödinger equation solution Wave Function (Schrodinger Solution) ψ (r, θ , φ) = R(r) Y (θ, φ( Radial Wave Function Angular Wave Function (Distance from nucleus) (Shape of orbital) Inorganic Chemistry Group 2021-2022  Significance of ψ ψn l m (r, θ, ϕ), = Rn l (r). Y l m(θ, ϕ) ψ2 = probability of finding an electron at a certain location. If either of these two components (R or Y) are zero, the total wavefunction is zero and the probability density (ψ2) there is also zero. Inorganic Chemistry Group 2021-2022 Quantum Numbers (zip codes for electrons) Schrödinger’s approach uses three quantum numbers (n, l , and ml ) to specify any wavefunction. Inorganic Chemistry Group 2021-2022 Principal quantum number (n) It determine the main energy level (shell) of electron. n=1, 2, 3, 4..... This number describes the energy of electron & its distance (radius) from the nucleus. Inorganic Chemistry Group 2021-2022 Principal quantum number (n) Inorganic Chemistry Group 2021-2022 Subsidiary (Azimuthal) (Angular momentum) quantum number ( l) l determines the subshells (orbitals) which are present within a shell. l value of l range from 0 to n - 1: l = 0, 1, 2, 3, 4, …, (n-1) l Determines the shape of subshell (orbital). Inorganic Chemistry Group 2021-2022 Subsidiary (Azimuthal) (Angular momentum) quantum number ( l) (ℓ) Historical Letter Historical Name 0 s sharp 1 p principal 2 d diffuse 3 f fundamental Inorganic Chemistry Group 2021-2022 Subsidiary (Azimuthal) (Angular momentum) quantum number (l) Inorganic Chemistry Group 2021-2022 Subsidiary (Azimuthal) (Angular momentum) quantum number (l) Inorganic Chemistry Group 2021-2022 Subsidiary (Azimuthal) (Angular momentum) quantum number (l) Inorganic Chemistry Group 2021-2022 Magnetic quantum number (ml ) ml determine the number of orbitals in each subshell ml = 2l + 1 ml take the values from − l to + l in integral steps: ml = - l, (- l +1), …, 0, …. (l -1), + l ml determine the direction of the orbitals in space. Inorganic Chemistry Group 2021-2022 Magnetic quantum number (ml ) Inorganic Chemistry Group 2021-2022 Allowed combination of quantum numbers n, l and ml Inorganic Chemistry Group 2021-2022 Magnetic quantum number (ml ) s-orbital , l =0 , ml = 0 Inorganic Chemistry Group 2021-2022 Magnetic quantum number (ml ) p-orbital , l = 1 , ml = -1, 0, +1 Inorganic Chemistry Group 2021-2022 Magnetic quantum number (ml ) d-orbital , l = 2 , ml = -2, -1, 0, +1, +2 Inorganic Chemistry Group 2021-2022 Magnetic quantum number (ml ) f-orbital , l = 3 , ml = +3, +2, +1, 0, -1, -2, -3 Inorganic Chemistry Group 2021-2022 Spin quantum number (s) or (ms) ms determines the spin and orientation of the magnetic field of the electrons. ms = ± ½ clockwise or anticlockwise = (-1/2) , (+1/2). Inorganic Chemistry Group 2021-2022 Spin quantum number (s) Inorganic Chemistry Group 2021-2022 Shape of s-orbital The probability depends on on R n,l (r) only. Spherical Inorganic Chemistry Group 2021-2022 Nodes for an orbital Nodes are points of zero electron density. ψ2 = probability of finding an electron at a certain location = 0. Total Nodes=n-1 Inorganic Chemistry Group 2021-2022 Shape of s-orbital Inorganic Chemistry Group 2021-2022 Probability density [ψ(r)]2 for 1s, 2s and 3s Inorganic Chemistry Group 2021-2022  Shape of p-orbital np orbital have (n - 2) radial nodes Inorganic Chemistry Group 2021-2022 Shape of d-orbital Inorganic Chemistry Group 2021-2022 Shape of f-orbital Inorganic Chemistry Group 2021-2022 Summary Inorganic Chemistry Group 2021-2022 (Lec. 06) Inorganic Chemistry Group 2021-2022  Outlines Relative energies of orbitals. Building up electronic configurations Electron configuration for elements and ions. Inorganic Chemistry Group 2021-2022 Orbitals Energies of multi-electron atoms The orbital having lower (n) value has lower energy. The orbital having lower (n+l) value has lower energy. Inorganic Chemistry Group 2021-2022 Orbitals Energies of multi-electron atoms Inorganic Chemistry Group 2021-2022 Orbitals Energies of multi-electron atoms Inorganic Chemistry Group 2021-2022 Orbitals Energies of multi-electron atoms The orbital having lower (n) value has lower energy. The orbital having lower (n+l) value has lower energy. Inorganic Chemistry Group 2021-2022 Why energy of 1s  2s  3s orbitals? lower (n + l ) lower energy For 1s, n + l = 1 + 0 = 1 For 2s , n + l = 2 + 0 = 2 For 3s, n + l = 3 + 0 =3 Inorganic Chemistry Group 2021-2022 Why energy of 2s  2p orbital? lower (n + l ) lower energy For 2s, n + l = 2 + 0 =2 For 2p , n + l = 2 + 1 =3 Inorganic Chemistry Group 2021-2022 Why energy of 4s  3d orbitals? lower (n + l ) lower energy For 4s, n + l = 4 + 0 =4 For 3d , n + l = 3 + 2 =5 Inorganic Chemistry Group 2021-2022 Building up electronic configurations Three rules to build up electronic configurations 1. Aufbau (building up) Principle 2. Pauli’s Exclusion Principle. 3. Hund’s Rule Inorganic Chemistry Group 2021-2022 Aufbau (Building-up) Principle The word 'Aufbau' is German for 'building up’. The Aufbau Principle, states that electrons will fill the lowest energy orbital first. The order of occupation is as follows: Inorganic Chemistry Group 2021-2022 Aufbau (Building-up) Principle Inorganic Chemistry Group 2021-2022 Pauli-Exclusion Principle Orbital can hold maximum of two electrons If two electrons in an orbital, must be opposite spins. Inorganic Chemistry Group 2021-2022 Hund's Rule (Empty bus seat rule) Within a sub-level, place one electron per orbital before pairing it. Or sublevel is singly occupied before any orbital is doubly occupied. Inorganic Chemistry Group 2021-2022 Hund's Rule Inorganic Chemistry Group 2021-2022 Hund's Rule Inorganic Chemistry Group 2021-2022 Electronic Configurations of Elements Inorganic Chemistry Group 2021-2022 Electron configuration and noble gases Inorganic Chemistry Group 2021-2022 Electron configuration of Lead (82Pb) Inorganic Chemistry Group 2021-2022 Electron configuration and noble gases Inorganic Chemistry Group 2021-2022 Electron configuration anomalies Inorganic Chemistry Group 2021-2022 Valence and Core Electrons Outer most level electrons Remaining inner electrons Inorganic Chemistry Group 2021-2022 Valence and Core Electrons Inorganic Chemistry Group 2021-2022