Chapter 7 Atomic Structure and the Periodic Table

1. Chapter 7 Atomic Structure and the Periodic Table • Electromagnetic Radiation = Light • What is Light? • Visible light is a particular kind of electromagnetic radiation • X-rays, UV, Infrared, Microwaves, and Radio waves are all light forms • Light is a form of Energy • All light travels in waves at “the speed of light” = c = 3 x 108 m/s

2. Characteristics of Light • Wavelength = distance between two peaks in a wave • l (lambda) is the symbol • Meters = m is the unit • Frequency = number of complete waves passing a given point per second • n (nu) is the symbol • Hertz = Hz = s-1 is the unit • Amplitude = A = measure of the intensity of the wave, “brightness” • The speed of light is constant: c =  x  • l and n are inversely proportional • If one increases, the other decreases • Their product is always the speed of light = c =  x  = 3 x 108 m/s

3. Example: What is the frequency of red light with l = 650 nm? • The Nature of Matter • Classical Physics ~1900 • Matter is composed of particles that have mass and a known position • Light is a form of energy without mass and uncertain position • These two phenomena were thought to be distinct • Planck’s Revelation • Studied the light given off by heated objects • Found that classical physics couldn’t explain his observations • Showed that light could be thought of as particles for certain applications • Energy can only be gained or lost as light in whole-number multiples • Particles of light have fixed energies = Basis of quantum theory • Energy is quantized = can only occur in discrete units = photons • The energy of the photon is directly proportional to the frequency of light (Higher frequency = More energy in photons)

4. 4. Example: How much E is being emitted by light of 450 nm? • Einstein’s Contribution • We can view any kind of light as a stream of particles = photons as well as a wave = Dual Nature of Light • Special Theory of Relativity: E = mc2 • Energy has mass that we can calculate from wavelength or frequency

5. de Broglie’s Equation showed that particles have wavelength too • Example: l = ? for e- (v = 1 x 107 m/s) and 0.10 kg ball (v = 35 m/s) • Electron wavelength is on the order of the spacing of atoms in a crystal; the ball’s wavelength is very tiny (it doesn’t behave much like a wave) • X-Ray Diffraction • 1. Diffraction = scattering light by an array of particles (rainbow on CD)

6. Diffraction proves electrons (particles) can behave like waves • Davisson and Germer aimed electrons at a Nickel crystal in 1927 • They observed a diffraction pattern, showing electrons are wavelike • Conclusions • Energy is a form of matter • Both matter and energy can behave as particles and as waves • Massive objects (baseball) behave mostly like particles • Tiny objects (electron, photons) behave mostly like waves • III. Atomic Spectra and the Bohr Model • Atoms can absorb or give off energy in the form of light • Light given off = emission spectrum • light energy gained = absorption spectrum • The light atoms give off or gain is of very specific wavelengths called a line spectrum • Each element has its own line spectrum which can be used to identify it

7. Energy and 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 • All possible energies, would result in continuous spectrum instead of lines Continuous Spectrum of white light Line spectrum of Hydrogen

8. Bohr’s model of the atom explained spectra of hydrogen • The Hydrogen electron moves around the nucleus in specific allowed circular orbits (Neils Bohr, 1885-1962) • Energy of an atom is related to the distance electron is from the nucleus • Energy of the atom is quantized • atom have specific energy states called energy levels • when atom gains energy, electrons “moves” to a higher quantum level • when atom loses energy, electrons “moves” to a lower energy level • lines in spectrum correspond to the difference in energy between levels

9. Atoms have a minimum energy called the ground state • Therefore, electrons do not crash into the nucleus • The ground state of H has its one electron 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 • We can calculate the energies of the Energy Levels of Hydrogen • Z = nuclear charge of the atom = +1 for Hydrogen • n = an integer (ground state has n = 1) • The negative sign indicates a favorable energy of interaction • If n = ∞, the interaction is zero (e- infinitely far away from nucleus) • We can also calculate the change in energy of a transition (Ex. n=1 to n=6) • Electron has gained energy going from ground to excited state • The energy would have to come from the absorption of light

10. We can calculate the wavelength of the absorbed photon • Example: Calculate the energy needed to remove the ground state e-. • A general equation for any two states can be derived • Solve for final n = ∞ and initial n = 1 • Problems with Bohr’s 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

11. Quantum Mechanical Atomic Model • Standing Waves • A string is limited to specific (quantized) vibrations • To Schrödinger (1887-1961), electrons quantized around a nucleus seemed similar • Experiments showed that electrons could be treated as waves • 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: • a. can only be solved for simple systems, but approximated for others • b. y = wavefunction, E = energy, H = operator • c. Many Energies can be found, each corresponding to an orbital • d. Orbitals correspond to a standing electron wave of a specific shape

12. 0.529Å • Results from the Quantum Mechanical Model • Heisenberg uncertainty principle: can’t know both position and momentum • Waves don’t have specific locations • Since electrons behave like waves, neither can electrons • y2 gives the probability of finding the electron in a given location • Probability of where the electron is around the nucleus • Imagine time-lapse picture of e- in n = 1 of a hydrogen atom • This plot gives the shape of the n = 1 orbital of Hydrogen = Sphere • Why isn’t the radial probability highest right next to the nucleus? • Probability is largest closest to nucleus • Volume of the “shell” is very small close to the nucleus • The sphere enclosing 90% of the electron probability = orbital picture