Chapter 5 Periodicity and Atomic Structure

Light and the Electromagnetic Spectrum Electromagnetic energy (“light”) is characterized by wavelength, frequency, and amplitude.

Light and the Electromagnetic Spectrum

Light and the Electromagnetic Spectrum Wavelength x Frequency = Speed = m s m s 1 c x c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value—speed of light. c = 3.00 x 10 8 s m

Examples ◦ The light blue glow given off by mercury streetlamps has a frequency of 6.88 x s -1 (or, Hz). What is the wavelength in nanometers?

Chapter 5/7© 2012 Pearson Education, Inc. Electromagnetic Energy and Atomic Line Spectra

Chapter 5/8© 2012 Pearson Education, Inc. Electromagnetic Energy and Atomic Line Spectra Line Spectrum: A series of discrete lines on an otherwise dark background as a result of light emitted by an excited atom

Electromagnetic Radiation and Atomic Spectra Individual atoms give off light when heated or otherwise excited energetically ◦ Provides clue to atomic makeup ◦ Consists of only few λ ◦ Line spectrum – series of discrete lines ( or wavelengths) separated by blank areas  E.g. Lyman series in the ultraviolet region

Chapter 5/10© 2012 Pearson Education, Inc. Electromagnetic Energy and Atomic Line Spectra Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen. 1 = R n2n2 1 m2m2 1 - Johann Balmer in 1885 discovered a mathematical relationship for the four visible lines in the atomic line spectra for hydrogen. 1 = R n2n R (Rydberg Constant) = x nm -1

The energy level of Hydrogen

Particlelike Properties of Electromagnetic Energy Photoelectric Effect : Irradiation of clean metal surface with light causes electrons to be ejected from the metal. Furthermore, the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal.

Examples Solar energy, which is produced by photovoltaic cells. These are made of semi-conducting material which produce electricity when exposed to sunlight it works on the basic principle of light striking the cathode which causes the emmision of electrons, which in turn produces a current.

Particlelike Properties of Electromagnetic Energy

E photon = h ν E Electromagnetic energy (light) is quantized. h (Planck’s constant) = x J s Einstein explained the effect by assuming that a beam of light behaves as if it were a stream of particles called photons. * 1mol of anything = 6.02 x 10 23

Emission of Energy by Atom How does atom emit light? ◦ Atoms absorbs energy ◦ Atoms become excited ◦ Release energy ◦ Higher-energy photon –>shorter wavelength ◦ Lower-energy photon -> longer wavelength

Examples What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 10 8 Hz? Calculate the wavelength of light that has energy 1.32 x J/photon Calculate the energy per photon of light with wavelength 650 nm

Particlelike Properties of Electromagnetic Energy Niels Bohr proposed in 1914 a model of the hydrogen atom as a nucleus with an electron circling around it. In this model, the energy levels of the orbits are quantized so that only certain specific orbits corresponding to certain specific energies for the electron are available.

Niels Bohr Model In each case the wavelength of the emitted or absorbed light is exactly such that the photon carries the energy difference between the two orbits Excitation by absorption of light and de-excitation by emission of light

Wavelike Properties of Matter The de Broglie equation allows the calculation of a “wavelength” of an electron or of any particle or object of mass m and velocity v. mv h = Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light. In other words, perhaps matter is wavelike as well as particlelike.

Examples Calculate the de Broglie wavelength of the “particle” in the following case ◦ A 25.0 bullet traveling at 612 m/s What velocity would an electron (mass = 9.11 x kg) need for its de Broglie wavelength to be that of red light (750 nm)?

Quantum Mechanics and the Heisenberg Uncertainty Principle 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.

Quantum Mechanics and the Heisenberg Uncertainty Principle Heisenberg Uncertainty Principle – both the position ( Δ x) and the momentum ( Δ mv) of an electron cannot be known beyond a certain level of precision 1.( Δ x) ( Δ mv) > h 4 π 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. Δ mv is small ii. Δ x (position of the electron) is large 4.If the exact position of the electron is known i. Δ mv is large ii. Δ x (position of the electron) is small

Wave Functions and Quantum Numbers 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.

Wave Functions and Quantum Numbers 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

Wave Functions and Quantum Numbers 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.

Wave Functions and Quantum Numbers 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.

Wave Functions and Quantum Numbers

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

The Shapes of Orbitals Node: A surface of zero probability for finding the electron.

The Shapes of Orbitals

Electron Spin and the Pauli Exclusion Principle 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.

Orbital Energy Levels in Multielectron Atoms

Electron Configurations of Multielectron Atoms Effective Nuclear Charge (Z eff ): The nuclear charge actually felt by an electron. Z eff = Z actual - Electron shielding

Electron Configurations of Multielectron Atoms 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

Electron Configurations of Multielectron Atoms 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.

Electron Configurations of Multielectron Atoms n = 1 s orbital (l = 0) 1 electron H: 1s11s1 Electron Configuration 1s21s2 n = 1 s orbital (l = 0) 2 electrons He:

Electron Configurations and the Periodic Table Valence Shell: Outermost shell or the highest energy. Br:4s 2 4p 5 Cl:3s 2 3p 5 Na:3s13s1 Li:2s12s1

Electron Configurations and the Periodic Table Give expected ground-state electron configurations (or the full electron configuration) 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)

Electron Configurations and Periodic Properties: Atomic Radii radiusrowradiuscolumn

Electron Configurations and Periodic Properties: Atomic Radii

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