Chapter Three Quantum Theory & the Structure of the Atom

Section 3.1 Energy & Types of Energy

Energy Types of Energy: Kinetic Potential Ex: Thermal Potential Ex: Chemical, Electrostatic Energy is measured in Joules (J); N*m; kg*m2/s2

Section 3.2 The Nature of Light

c = ln (Know these!) Light (m, nm); n (nu) = frequency (1/s, s-1, Hz) Light is typically described as traveling in waves (similar to water); All electromagnetic (EM) waves (including light) are made of two components: electric and magnetic EM waves travel at the speed of light, c (2.998 x 108) c = ln (Know these!) c = speed of light; l (lambda) = wavelength (m, nm); n (nu) = frequency (1/s, s-1, Hz)

Light and the EM Spectrum EM waves

EM Spectrum Different colors of light correspond to different wavelengths in the visible portion of the EM spectrum. Two wavelengths (l) are shown below. Determine the frequency (n) for each wave. Blue light Red light 1 nm = 1 x 10-9 m OR 1 x 109 nm = 1 m

Double Slit Experiment Electrons behave as particles as well as waves Behave differently if being observed

Section 3.3 Quantum Theory

Describing Atoms Classical descriptions: New view of atomic behavior Dalton: atoms are hard particles, all atoms of the same element are the same Energy is continuous Planetary model of atom New view of atomic behavior Planck: Blackbody radiation – heat solids to red or white heat, matter did not emit energy continuously; in whole-number multiples of certain quantities Matter absorbs or emits energies in packets - quanta

From Classical to Quantum Theory Einstein used Planck’s theory to observe metals reacting to different colors of light – Photoelectric Effect: electrons are ejected from the surface of certain metals exposed to light at a certain minimum frequency Example: Blue light (n = 6.7 x 1014 Hz) causes Na to emit electrons, red light (n = 4.0 x 1014 Hz) does not

Wave-Particle Duality Based on photoelectric effect, light acts as a wave but also exists as a stream of particles called photons Energy of photons is proportional to frequency, inversely proportional to wavelength h = 6.626 x 10-34 J•s J = kg • m2 / s2

Calculation Practice c = ln;E = hn 1) Which has a higher frequency: light from a red stoplight with a wavelength of 750 nm or a yellow light with a wavelength of 600 nm? 2) What is the wavelength of a radio station’s waves transmitting at a frequency of 101.5 MHz (megahertz)? (FM radio waves range from 30 – 300 MHz.) 3) Red lights at traffic stops have wavelengths of about 650 nm. What is the frequency (in Hz) of this light? 4) Calculate the energy (in Joules) of a photon with a wavelength of 5.00 x 104 nm (infrared region). Answers: yellow, 2.956 m, 4.62 x 1014 Hz, 3.98 x 10-21 J

Group Quiz #1 1) The energy of a photon is 5.87 x 10-20 J. What is the frequency of the photon? 2) What is the wavelength of an electron that travels at 34.7 m/s and has a mass of 9.11 x 10-31 kg?

Section 3.4 Bohr’s Theory of the Hydrogen Atom

Bohr’s Model of the Atom Bohr sought to reconcile these views of the electron. Developed the planetary analogy of atoms. Electrons orbit around the nucleus like planets around the sun. Electrons travel in discrete, quantized circular orbits; like going up or down stairs. Each orbit has a specific energy associated with it, labeled as n = 1, 2, etc. Ground state is the lowest energy level for an atom (n = 1).

Bohr’s Model of the Atom

Bohr’s Model of the Atom When electrons ABSORB energy, they “jump” energy levels. When electrons RELEASE energy (in the form of EM radiation), they “drop” energy levels. Every drop corresponds to a different wavelength n = 1  n = 2 is the biggest jump

Emission Spectra of Elements http://www.wwnorton.com/college/chemistry/chemconnections/BlueLight/pages/elements.html Emission Spectra of Elements Figure 7.8

Transitions between Energy Levels

Section 3.5 Wave Properties of Matter

Wavelike Properties of Matter de Broglie: If light can behave like a wave and a particle, then matter (i.e., electrons) can behave like a wave Can calculate wavelength for all matter if we know its velocity (use v instead of c): l = h / m v (This is the de Broglie equation.) h = Planck’s constant, m = mass (electron’s have constant mass: 9.11x10-31 kg), v = velocity (speed)

Waves of Electrons

Section 3.6 Quantum Mechanics

Heisenberg Uncertainty Principle If electrons have wavelike properties, then we can’t know both its position and velocity. REASON: In order to determine the position of an electron, we hit it with a photon of light, but this will change its position and velocity.

Quantum Mechanical Model The Bohr model worked well for hydrogen, but failed for elements with more than one proton and one electron. Quantum Mechanics was developed (by Schrödinger in the 1920’s) to describe the motion of subatomic particles Did not attempt to describe position of particles; used mathematical equations to describe the probability of finding the particles The probability density (map of likely locations) is the “electron cloud”

Atomic Orbitals The region of highest probability for finding an electron is an “electron cloud”. This region of high probability is called an atomic orbital. Each orbital holds at most 2 electrons. 27

Section 3.7 & 3.8 Quantum Numbers

Quantum Numbers There are 4 quantum number that describe the size, shape, and location of electrons We use these numbers to describe where electrons are found for an atom. Can also use the periodic table!!! 29

Quantum Numbers Quantum Number Symbol What it tells us A.K.A. Numbers Example Principal Quantum Number n Energy level (distance from nucleus) Energy level or Shell n = 1, 2, 3, etc. n = 2 is 2nd energy level Angular Momentum Quantum Number l Shape of orbital Subshells l = 0, 1, 2, 3, n-1 l = 1 is p subshell Magnetic Quantum Number ml Orientation of orbital Orbital ml = -l to +l Spin Quantum Number ms Spin of the electron N/A ms = +1/2 or -1/2

Orbitals and Quantum Numbers 31

Shapes of Orbitals

Orbitals and Quantum Numbers

Quantum Numbers

Orbitals and Quantum Numbers

Group Quiz #2 1) What is the maximum number of: a) electrons allowed in the 2px orbital? b) subshells allowed in the 4th shell? c) electrons allowed in the 3d subshell? d) electrons allowed in the 4d subshell? e) electrons allowed in the 3p subshell? f) electrons allowed in the 3rd shell?

Section 3.9 & 3.10 Electron Configurations

Electron Configurations Arrangement of subshells in the Periodic Table 38

Energies of Orbitals

Aufbau Principle Aufbau principle: start with the nucleus and empty orbitals, then “build” up the electron configuration using orbitals of increasing energy. 40

Writing Electron Configurations Write electron configurations for the following atoms. Pt U

Electron Configuration Some exceptions to the Aufbau order… What are the expected electron configurations for Cr and Cu? Filled and half-filled d subshells seem to be especially stable. Cr: 1s2 2s2 2p6 3s2 3p6 4s1 3d5 Also true for Mo and W Cu: 1s2 2s2 2p6 3s2 3p6 4s1 3d10 Also true for Ag and Au 42

Shorthand Notation Rather than writing out complete electron configurations, we can use the previously filled shell (noble gas) and show the valence electrons (v. e.): P: 1s2 2s2 2p6 3s2 3p3  [Ne] 3s2 3p3 Write the shorthand notation for: Sr Fe

Electron Configurations

Valence Electrons Electrons in the outermost shell. 1s2 2s2 2p6 1s2 2s2 2p6 3s2 3p5 Identify the valence electrons (v. e.) in the following configurations: 1s2 2s2 2p6 3s2 1s2 2s2 2p63s23p4 1s2 2s2 45

Hund’s Rule If two or more orbitals (i.e., a p or d orbital) with the same energy are available, one electron goes into each orbital until they have to pair up. “Fighting siblings” rule For example, an atom with 2 p electrons: 1 electron will go into the first orbital (px), the next electron will go into the second orbital (py).

Pauli Exclusion Principle Pauli Exclusion Principle: no two electrons can have the same values of all 4 quantum numbers Describes what happens when electrons share an orbital. Only two electrons can occupy a single orbital and they must have opposite spin (i.e., the 4th quantum number). The first electron is designated as positive spin (up arrow), the second electron in that orbital has negative spin (down arrow). 47

Orbital Diagrams Orbital diagrams are pictorial representations of electron configurations. 48

Group Quiz #3 Write electron configurations for the following elements (short-hand notation) as well as Indicate the number of v.e. for each element. Silver (Ag) Zinc (II) (Zn2+) Americium (Am)