Chapter 7 Quantum Theory and Atomic Structure
Outline 1. The Nature of Light 2. Atomic Spectra 3. The Wave-Particle Duality of Matter and Energy 4. The Quantum-Mechanical Model of the Atom 3 September 2013 2
Wave Nature of Light Wavelength (l) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency (n) is the number of cycles the wave undergoes per second. 3 September 2013 3
Electromagnetic Radiation 3 September 2013 4
Interconverting l and n Some diamonds appear yellow because they contain nitrogen compounds that absorb purple light of frequency 7.23 x 10 14 Hz. Calculate the wavelength (in nm and Å) of the absorbed light. Assume that radiation travels at 3.00 x 10 8 m/s. 3 September 2013 5
Particle Nature of Light Discovered in the early 1900 s while physicists tried to explain three mysteries: Blackbody Radiation Photoelectric Effect Atomic Spectra 3 September 2013 6
Mystery # 1: Blackbody Radiation Blackbody: an idealised object that absorbs all electromagnetic radiation falling on it. All solids heated above T > 0 K emit electromagnetic radiation. Higher T higher frequencies (lower wavelength) and higher intensities of light. 1000 K 5000 K 9000 K 3 September 2013 7
Mystery # 1: Blackbody Radiation Max Planck proposed that energy (light) is emitted or absorbed in discrete units (quantum). Energy of an atom is quantized: it exists in fixed quantities, rather than being continuous. E = nhn Energy (in J) n: positive integer h: Planck s constant (6.626 x 10-34 Js) n: frequency 3 September 2013 8
Mystery # 2: Photoelectric Effect When a photoelectric tube is bombarded with electromagnetic radiation (light), only specific frequencies eject electrons from the surface of the light sensitive plate to generate current. 3 September 2013 9
Mystery # 2: Photoelectric Effect Albert Einstein proposed that light itself is made of particles, or quantized into small bundles of electromagnetic energy photons Each atom changes its energy whenever it absorbs or emits one photon whose energy is fixed by its n E photon = hn 3 September 2013 10
Learning Check Calculate the energies of one photon of ultraviolet (λ = 1 x 10-8 m), visible (λ = 5 x 10-7 m), and infrared (λ = 1 x 10-4 m) light. What do the answers indicate about the relationship between the wavelength and energy of light? E = hν h = 6.626 x 10-34 Js speed of light, c = 3.00 x 10 8 m/s 3 September 2013 11
Mystery # 3: Atomic Spectra Narrow bands of colors of light are emitted when gases are excited by high voltage. The colors are characteristic and reproducible for different elements. Generated light is dispersed into its component λ. High voltage tube containing H 2 (g) 3 September 2013 12
All elements display a characteristic emission spectra that we can use to fingerprint all elements. 3 September 2013 13
Flame tests cause a similar electron excitement characteristic to each element. The color helps us identify the elements. Hydrogen Helium Lithium Sodium Potassium 3 September 2013 14
Chemistry of Fireworks 3 September 2013 15
Mystery # 3: Atomic Spectra How could scientists account for the lines if atomic theory and classical physics were correct? How does the emission spectrum relate the atomic and electronic structure of the H atom? 3 September 2013 16
Early Explanation In 1885, Rydberg developed a generalized but empirical mathematical relationship between ν and n for all the lines of hydrogen emission spectrum. 1 1 Rydberg equation = R - l n 2 1 1 n 2 2 3 September 2013 17
Bohr Model of the Hydrogen Atom 1. The H atom has only certain energy levels called stationary states. Each state is associated with a fixed circular orbit of the electron around the nucleus. The higher the energy level, the farther the orbit is from the nucleus. When the H electron is in the first orbit, the atom is in its lowest energy state, called the ground state. 3 September 2013 19
Bohr Model of the Hydrogen Atom 2. The atom does not radiate energy while in one of its stationary states. 3. The atom changes to another stationary state only by absorbing or emitting a photon. The energy of the photon (hn) equals the difference between the energies of the two energy states. When the electron is in any orbit higher than n = 1, the atom is in an excited state. 3 September 2013 20
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Practice Exercise What is the wavelength of a photon (in nm) emitted during a transition from the n i = 5 state to the n f = 2 state in the hydrogen atom? 1 The energy of a level: E = R H n 2 The difference in energy between any two levels: E = R H 1 R H = 2.18 x 10 18 J n i 2 1 n f 2 3 September 2013 23
Announcements Quiz #6 on Sept 5. Chapter 7 Problem Set: 2, 6, 7, 11, 17, 20, 32, 39, 41, 43, 44, 46, 48, 60. Problem Solving Class Schedule: Ch 7 D F 12:30 1:30 SOM 202 Ch 7 E F 11:30 12:30 CTC 102 Ch 7 F M 12:30 1:30 CTC 104 Ch 7 G W 2:30 3:30 SOM 105 Ch 7 H-K MWF 3:30 4:30 C 109 Ch 7 L T 4:30 5:30 C 114 Ch 7 C M 2:30-3:30 SOM 105 3 September 2013 25