Chapter 5 Periodicity and Atomic Structure

Q UANTUM M ECHANICS AND THE H EISENBERG U NCERTAINTY P RINCIPLE In 1926 Erwin Schrödinger proposed the quantum mechanical model of the atom which focuses on the wavelike properties of the electron. In 1927 Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle.

Q UANTUM M ECHANICS AND THE H EISENBERG U NCERTAINTY P RINCIPLE Heisenberg Uncertainty Principle – both the position (Δx) and the momentum (Δmv) of an electron cannot be known beyond a certain level of precision 1.(Δx) (Δmv) > h 4π 2. Cannot know both the position and the momentum of an electron with a high degree of certainty 3.If the momentum is known with a high degree of certainty i.Δmv is small ii.Δ x (position of the electron) is large 4.If the exact position of the electron is known i.Δmv is large ii.Δ x (position of the electron) is small

W AVE F UNCTIONS AND Q UANTUM N UMBERS Probability of finding electron in a region of space (  2 ) Wave equation Wave function or orbital (  ) solve A wave function is characterized by three parameters called quantum numbers, n, l, m l.

W AVE F UNCTIONS AND Q UANTUM N UMBERS Principal Quantum Number (n) Describes the size and energy level of the orbital Commonly called shell Positive integer (n = 1, 2, 3, 4, …) As the value of n increases: The energy increases The average distance of the e - from the nucleus increases

W AVE F UNCTIONS AND Q UANTUM N UMBERS Angular-Momentum Quantum Number (l) Defines the three-dimensional shape of the orbital Commonly called subshell There are n different shapes for orbitals If n = 1 then l = 0 If n = 2 then l = 0 or 1 If n = 3 then l = 0, 1, or 2 etc. Commonly referred to by letter (subshell notation) l = 0s (sharp) l = 1p (principal) l = 2d (diffuse) l = 3f (fundamental) etc.

W AVE F UNCTIONS AND Q UANTUM N UMBERS Magnetic Quantum Number (m l ) Defines the spatial orientation of the orbital There are 2l + 1 values of m l and they can have any integral value from -l to +l If l = 0 then m l = 0 If l = 1 then m l = -1, 0, or 1 If l = 2 then m l = -2, -1, 0, 1, or 2 etc.

W AVE F UNCTIONS AND Q UANTUM N UMBERS

Identify the possible values for each of the three quantum numbers for a 4 p orbital. Give orbital notations for electrons in orbitals with the following quantum numbers: a) n = 2, l = 1, m l = 1b) n = 4, l = 0, m l =0 Give the possible combinations of quantum numbers for the following orbitals: A 3s orbitalb) A 4f orbital

T HE S HAPES OF O RBITALS Node: A surface of zero probability for finding the electron.

T HE S HAPES OF O RBITALS

E LECTRON S PIN AND THE P AULI E XCLUSION P RINCIPLE Electrons have spin which gives rise to a tiny magnetic field and to a spin quantum number (m s ). Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers.

O RBITAL E NERGY L EVELS IN M ULTIELECTRON A TOMS

E LECTRON C ONFIGURATIONS OF M ULTIELECTRON A TOMS Effective Nuclear Charge (Z eff ): The nuclear charge actually felt by an electron. Z eff = Z actual - Electron shielding

E LECTRON C ONFIGURATIONS OF M ULTIELECTRON A TOMS Electron Configuration: A description of which orbitals are occupied by electrons. 1s 2 2s 2 2p 6 …. Degenerate Orbitals: Orbitals that have the same energy level. For example, the three p orbitals in a given subshell. 2px 2py 2pz Ground-State Electron Configuration: The lowest-energy configuration. 1s 2 2s 2 2p 6 …. Orbital Filling Diagram: using arrow(s) to represent occupied in an orbital

E LECTRON C ONFIGURATIONS OF M ULTIELECTRON A TOMS Aufbau Principle (“building up”): A guide for determining the filling order of orbitals. Rules of the aufbau principle: 1.Lower-energy orbitals fill before higher-energy orbitals. 2.An orbital can only hold two electrons, which must have opposite spins (Pauli exclusion principle). 3.If two or more degenerate orbitals are available, follow Hund’s rule. Hund’s Rule: If two or more orbitals with the same energy are available, one electron goes into each until all are half-full. The electrons in the half- filled orbitals all have the same spin.

E LECTRON C ONFIGURATIONS OF M ULTIELECTRON A TOMS Cha pter 5/19 Copyright © 2008 Pearson Prentice Hall, Inc. n = 1 s orbital (l = 0) 1 electron H: 1s11s1 Electron Configuration

E LECTRON C ONFIGURATIONS OF M ULTIELECTRON A TOMS Cha pter 5/20 Copyright © 2008 Pearson Prentice Hall, Inc. 1s21s2 n = 1 s orbital (l = 0) 2 electrons H: He: Electron Configuration 1s11s1

E LECTRON C ONFIGURATIONS OF M ULTIELECTRON A TOMS Cha pter 5/21 Copyright © 2008 Pearson Prentice Hall, Inc. n = 2 s orbital (l = 0) 1 electrons 1s 2 2s 1 H: Li: Lowest energy to highest energy He: Electron Configuration 1s21s2 1s11s1

E LECTRON C ONFIGURATIONS AND THE P ERIODIC T ABLE Cha pter 5/22 Copyright © 2008 Pearson Prentice Hall, Inc. Valence Shell: Outermost shell or the highest energy. Br:4s 2 4p 5 Cl:3s 2 3p 5 Na:3s13s1 Li:2s12s1

E LECTRON C ONFIGURATIONS AND THE P ERIODIC T ABLE Give expected ground-state electron configurations for the following atoms, draw – orbital filling diagrams and determine the valence shell O (Z = 8) Ti (Z = 22) Sr (Z = 38) Sn (Z = 50) Cha pter 5/23 Copyright © 2008 Pearson Prentice Hall, Inc.

E LECTRON C ONFIGURATIONS AND P ERIODIC P ROPERTIES : A TOMIC R ADII Cha pter 5/24 Copyright © 2008 Pearson Prentice Hall, Inc. radiusrowradiuscolumn

E LECTRON C ONFIGURATIONS AND P ERIODIC P ROPERTIES : A TOMIC R ADII Cha pter 5/25 Copyright © 2008 Pearson Prentice Hall, Inc.

E XAMPLES Arrange the elements P, S and O in order of increasing atomic radius