PF1009 2024 10 Quantum Numbers and Atomic Orbitals PDF

Pharmaceutical Chemistry Quantum Numbers and Atomic Orbitals Dr. J.J. Keating 1  Orbitals and Bonding Electrons are not discrete particles, but have wavelike properties. Heisenberg uncertainty principle – due to the wave...

Pharmaceutical Chemistry Quantum Numbers and Atomic Orbitals Dr. J.J. Keating 1  Orbitals and Bonding Electrons are not discrete particles, but have wavelike properties. Heisenberg uncertainty principle – due to the wavelike character of an electron, it is impossible to pinpoint the precise location of an electron. The mathematical expression that summarises where an electron is likely to be found is called its wavefunction. Atomic orbital – the wavefunction of an electron in an atom. It is the region in space in which there is a high probability of finding an electron. Each atomic orbital is defined by three quantum numbers: Principal (n) – labels the shell Azimuthal (l) – labels the subshell (s, p, d, f) Magnetic (ml) – labels orbitals of the subshells Spin-magnetic (ms) – +½, –½ - labels spin state of electrons within orbitals. All orbitals with the same value of n belong to the same shell. Average distance of an electron from the nucleus increases as n increases. 2  Electron Spin Electrons have two spin states, represented by the arrows ↑ (up) and ↓ (down). Both spin states distinguished by ms (the fourth quantum number – spin magnetic). ms can have only two values +½ for an ↑ electron –½ for a ↓ electron. 3  Electronic Configurations – Quantum Numbers Every electron surrounding the nucleus of an element can be assigned a set of four unique quantum numbers in the order: n, l, ml, ms Quantum Name What it Possible values Notes number labels n principal shell natural numbers Except for d-orbitals, the shell number matches number excluding 0: the row of the periodic table. 1, 2, 3, …. l azimuthal sublevel: natural numbers including 0 = s-orbital in the s-sublevel s, p, d, f 0 up to (n – 1): 1 = p-orbitals in the p-sublevel 0, 1, 2, …. (n – 1) 2 = d-orbitals in the d-sublevel 3 = f-orbitals in the f-sublevel sublevel ml magnetic specific integers between and l = 0 (s): 2 e– in one s-orbital (ml = 0) orbitals in including –l and +l: l = 1 (p): 2 e– in each of three p-orbitals: a sublevel –l, –l + 1, ….,+l – 1 +l (px (ml = –1), py (ml = 0), pz (ml = +1)) l = 2 (d): 2 e– in each of five d-orbitals (dxy (ml = –2), dxz (ml = –1), dyz (ml = 0), dx2 – y2 (ml = +1), dz2 (ml = +2)) ms spin electron two rational numbers: Electron spin pairs in any one orbital must be magnetic spin +½, –½ opposite 3, 1, –1, +½ 4  Orbital Energies In atoms with many electrons, electron- electron repulsions cause the energy of a d subshell (sublevel) to be higher than a s subshell (sublevel) of the next higher shell. An s electron is found very close to the nucleus – an s electron penetrates closer to the nucleus. Each electron is shielded from the full attraction of the nucleus by the other electrons in the atom – the effective nuclear charge is less than the actual charge. The spins of two electrons are paired if one is ↑ and the other is ↓. Paired spins are denoted ↑↓. No two electrons in an atom can have the same set of four quantum numbers. 5  s-Orbitals Spherical. An electron with a probability distribution given by a 1s orbital is said to occupy a 1s orbital and be a 1s electron. As an s-orbital is spherical, it can have only one orientation → one s-orbital per shell. Surface of the orbital = boundary surface. Surface of the sphere is the boundary within which there is about a 90% probability of finding the electron. 6  s-Orbitals All s-orbitals are spherical in shape but differ in size: 1s > 2s > 3s. r = distance from the nu Nodes are regions in orbitals where the wavefunction has a value of zero. Total number of nodes = n – 1 (n = principal quantum number) Thus, every orbital with n > 1 has at least one node. P r P r P = Probability Density. The probability of finding an electron P at a distance r from any direction r from the nucleus. r = distance from the nucleus (pm) (10–12 m). 7  p-Orbitals Dumbbell shapes. Labelled with the name of the axis they lie along. 8  d-Orbitals Four of the d-orbitals have a double dumbbell shape. The fifth orbital (dz2) is a doughnut shape (torus) with a dumbbell perpendicular to the torus and passing through it. 9