Modern Atomic Theory Chapter 10

Electromagnetic Radiation Classical physics says matter made up of particles, energy travels in waves Electromagnetic Radiation is radiant energy, both visible and invisible Electromagnetic radiation travels in waves All waves are characterized by their velocity, wavelength, amplitude, and the number of waves that pass a point in a given time 2

Figure 10.1 (a): A light wave

Electromagnetic Waves velocity = c = speed of light 2.997925 x 108 m/s all types of light energy travel at the same speed amplitude = A = measure of the intensity of the wave, “brightness” wavelength =  = distance between two consecutive peaks or troughs in a wave generally measured in nanometers (1 nm = 10-9 m) same distance for troughs frequency = = the number of waves that pass a point in space in one second generally measured in Hertz (Hz), 1 Hz = 1 wave/sec = 1 sec-1 c =  x  3

Figure 10.2: The different wavelengths of electromagnetic radiation

Planck’s Revelation Showed that light energy could be thought of as particles for certain applications Stated that light came in particles called quanta or photons Particles of light have fixed amounts of energy Basis of quantum theory The energy of the photon is directly proportional to the frequency of light Higher frequency = More energy in photons 5

Figure 10.3: Electromagnetic radiation

Problems with Rutherford’s Nuclear Model of the Atom Electrons are moving charged particles Moving charged particles give off energy Therefore the atom should constantly be giving off energy And the electrons should crash into the nucleus and the atom collapse!! 6

Atomic Spectra Atoms which have gained extra energy release that energy in the form of light The light atoms give off or gained is of very specific wavelengths called a line spectrum light given off = emission spectrum light energy gained = absorption spectrum extends to all regions of the electromagnetic spectrum Each element has its own line spectrum which can be used to identify it 7

Figure 10.5: Absorption and Emission Processes

Figure 10.6: When an excited H atom returns to a lower energy level, it emits a photon that contains the energy released by the atom

Atomic Spectra The line spectrum must be related to energy transitions in the atom. Absorption = atom gaining energy Emission = atom releasing energy Since all samples of an element give the exact same pattern of lines, every atom of that element must have only certain, identical energy states The atom is quantized If the atom could have all possible energies, then the result would be a continuous spectrum instead of lines 8

Figure 10.7: When excited hydrogen atoms return to lower energy states, they emit photons of certain energies, and thus certain colors

Figure 10.9: Each photon emitted by an excited hydrogen atom corresponds to a particular energy change in the hydrogen atom

Bohr’s Model Explained spectra of hydrogen Energy of atom is related to the distance electron is from the nucleus Energy of the atom is quantized atom can only have certain specific energy states called quantum levels or energy levels when atom gains energy, electron “moves” to a higher quantum level when atom loses energy, electron “moves” to a lower energy level lines in spectrum correspond to the difference in energy between levels 9

Figure 10. 10: (a) Continuous energy levels Figure 10.10: (a) Continuous energy levels. (b) Discrete (quantized) energy levels.

Figure 10.11: The difference between continuous and quantized energy levels

Bohr’s Model Atoms have a minimum energy called the ground state therefore they do not crash into the nucleus The ground state of hydrogen corresponds to having its one electron in an energy level that is closest to the nucleus Energy levels higher than the ground state are called excited states the farther the energy level is from the nucleus, the higher its energy To put an electron in an excited state requires the addition of energy to the atom; bringing the electron back to the ground state releases energy in the form of light 10

Figure 10.13: The Bohr model of the hydrogen atom

Bohr’s Model Distances between energy levels decreases as the energy increases light given off in a transition from the second energy level to the first has a higher energy than light given off in a transition from the third to the second, etc. Electrons “orbit” the nucleus much like planets orbiting the sun 1st energy level can hold 2e-1, the 2nd 8e-1, the 3rd 18e-1, etc. farther from nucleus = more space = less repulsion The highest energy occupied ground state orbit is called the valence shell 11

Figure 10.9: Each photon emitted by an excited hydrogen atom corresponds to a particular energy change in the hydrogen atom

Problems with the Bohr Model Only explains hydrogen atom spectrum and other 1 electron systems Neglects interactions between electrons Assumes circular or elliptical orbits for electrons - which is not true 12

Wave Mechanical Model of the Atom Experiments later showed that electrons could be treated as waves just as light energy could be treated as particles de Broglie The quantum mechanical model treats electrons as waves and uses wave mathematics to calculate probability densities of finding the electron in a particular region in the atom Schrödinger Wave Equation can only be solved for simple systems, but approximated for others 13

Figure 10.15: The probability map, or orbital, that describes the hydrogen electron in its lowest possible energy state

Orbitals Solutions to the wave equation give regions in space of high probability for finding the electron - these are called orbitals usually use 90% probability to set the limit three-dimensional Orbitals are defined by three integer terms that are added to the wave equation to quantize it - these are called the quantum numbers Each electron also has a fourth quantum number to represent the direction of spin 14

Figure 10.16: The hydrogen 1s orbital

Orbitals and Energy Levels Principal energy levels identify how much energy the electrons in the orbital have n higher values mean orbital has higher energy higher values mean orbital has farther average distance from the nucleus Each principal energy level contains one or more sublevels there are n sublevels in each principal energy level each type of sublevel has a different shape and energy s < p < d < f Each sublevel contains one or more orbitals s = 1 orbital, p = 3, d = 5, f = 7 15

Figure 10.17: The first four principal energy levels in the hydrogen atom

Figure 10.18: Principal levels can be divided into sublevels

Figure 10.19: Principal level 2 shown divided into the 2s and 2p sublevels

Figure 10.20: The relative sizes of the 1s and 2s orbitals of hydrogen

Figure 10.21: The three 2p orbitals: (a) 2px, (b) 2pz, (c) 2py.

Figure 10.22: A diagram of principal energy levels 1 and 2 showing the shapes of orbitals that compose the sublevels

Figure 10.23: The relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen

Figure 10.24: The shapes and labels of the five 3d orbitals

Pauli Exclusion Principle No orbital may have more than 2 electrons Electrons in the same orbital must have opposite spins s sublevel holds 2 electrons p sublevel holds 6 electrons d sublevel holds 10 electrons f sublevel holds 14 electrons 16

Orbitals, Sublevels & Electrons for a many electron atom, build-up the energy levels, filling each orbital in succession by energy ground state 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p degenerate orbitals are orbitals with the same energy each p sublevel has 3 degenerate p orbitals each d sublevel has 5 degenerate d orbitals each f sublevel has 7 degenerate f orbitals 17

Figure 10.28: A box diagram showing the order in which orbitals fill to produce the atoms in the periodic table

Hund’s Rule for a set of degenerate orbitals, half fill each orbital first before pairing highest energy level called the valence shell electrons in the valence shell called valence electrons electrons not in the valence shell are called core electrons often use symbol of previous noble gas to represent core electrons 1s22s22p6 = [Ne] 18

Electron Configuration Elements in the same column on the Periodic Table have Similar chemical and physical properties Similar valence shell electron configurations Same numbers of valence electrons Same orbital types Different energy levels 19

s1 s2 d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 p1 p2 p3 p4 p5 p6 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 1 2 3 4 5 6 7 20

Figure 10.25: The electron configurations in the sublevel last occupied for the first eighteen elements

The Modern Periodic Table Columns are called Groups or Families Rows are called Periods Each period shows the pattern of properties repeated in the next period Main Groups = Representative Elements Transition Elements Bottom rows = Lanthanides and Actinides really belong in Period 6 & 7 21

Figure 10.26: Partial electron configurations for the elements potassium through krypton

Figure 10.27: The orbitals being filled for elements in various parts of the periodic table

Metallic Character Metals Metalloids Nonmetals malleable & ductile shiny, lustrous conduct heat and electricity most oxides basic and ionic form cations in solution lose electrons in reactions - oxidized Metalloids Also known as semi-metals Show some metal and some nonmetal properties Nonmetals brittle in solid state dull electrical and thermal insulators most oxides are acidic and molecular form anions and polyatomic anions gain electrons in reactions - reduced 22

Figure 10.31: The classification of elements as metals, nonmetals, and metalloids

Metallic Character Metals are found on the left of the table, nonmetals on the right, and metalloids in between Most metallic element always to the left of the Period, least metallic to the right, and 1 or 2 metalloids are in the middle Most metallic element always at the bottom of a column, least metallic on the top, and 1 or 2 metalloids are in the middle of columns 4A, 5A, and 6A 23

Reactivity Reactivity of metals increases to the left on the Period and down in the column follows ease of losing an electron Reactivity of nonmetals (excluding the noble gases) increases to the right on the Period and up in the column 24

Trend in Ionization Energy Minimum energy needed to remove a valence electron from an atom gas state The lower the ionization energy, the easier it is to remove the electron metals have low ionization energies Ionization Energy decreases down the group valence electron farther from nucleus Ionization Energy increases across the period left to right 25

Trend in Atomic Size Increases down column Decreases across period valence shell farther from nucleus Decreases across period left to right adding electrons to same valence shell valence shell held closer because more protons in nucleus 26

Figure 10. 32: Relative atomic sizes for selected atoms Figure 10.32: Relative atomic sizes for selected atoms. Note that atomic size increases down a group and decreases across a period