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Chapter 13 Electrons in Atoms Section 13.1 Models of the Atom OBJECTIVES: Summarize the development of atomic theory. Section 13.1 Models of the Atom OBJECTIVES: Explain the significance of quantized energies of electrons as they relate to the quantum mechanical model of the atom. Greek Idea Democritus Matter is made up of solid indivisible particles John Dalton - one type of atom for each element J. J. Thomson’s Model Discovered electrons Atoms were made of positive stuff Negative electron floating around “Plum-Pudding” model Ernest Rutherford’s Model Discovered dense positive piece at the center of the atom- nucleus Electrons would surround it Mostly empty space “Nuclear model” Niels Bohr’s Model He had a question: Why don’t the electrons fall into the nucleus? Move like planets around the sun. In circular orbits at different levels. Amounts of energy separate one level from another. “Planetary model” Bohr’s planetary model Energy level of an electron analogous to the rungs of a ladder electron cannot exist between energy levels, just like you can’t stand between rungs on ladder Quantum of energy required to move to the next highest level The Quantum Mechanical Model Energy is quantized. It comes in chunks. A quanta is the amount of energy needed to move from one energy level to another. Since the energy of an atom is never “in between” there must be a quantum leap in energy. Erwin Schrodinger derived an equation that described the energy and position of the electrons in an atom The Quantum Mechanical Model Things that are very small behave differently from things big enough to see. The quantum mechanical model is a mathematical solution It is not like anything you can see. The Quantum Mechanical Model Has energy levels for electrons. Orbits are not circular. It can only tell us the probability of finding an electron a certain distance from the nucleus. The Quantum Mechanical Model The atom is found inside a blurry “electron cloud” A area where there is a chance of finding an electron. Draw a line at 90 % Think of fan blades Atomic Orbitals Principal Quantum Number (n) = the energy level of the electron. Within each energy level, the complex math of Schrodinger’s equation describes several shapes. These are called atomic orbitals - regions where there is a high probability of finding an electron. Sublevels- like theater seats arranged in sections Two representations of the hydrogen 1s, 2s, and 3s orbitals. Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals. Representation of the 3d orbitals. Representation of the 4f orbitals in terms of their boundary surface. Summary # of Max Starts at shapes electrons energy level s 1 2 1 p 3 6 2 d 5 10 3 f 7 14 4 By Energy Level First Energy Level Second Energy only s orbital Level only 2 electrons s and p orbitals 1s 2 are available 2 in s, 6 in p 2 6 2s 2p 8 total electrons By Energy Level Third energy level Fourth energy s, p, and d level orbitals s,p,d, and f 2 in s, 6 in p, and orbitals 10 in d 2 in s, 6 in p, 10 2 6 10 3s 3p 3d in d, ahd 14 in f 4s 24p64d104f14 18 total electrons 32 total electrons By Energy Level Any more than The orbitals do the fourth and not not fill up in a all the orbitals will neat order. fill up. The energy levels You simply run overlap out of electrons Lowest energy fill first. Section 13.2 Electron Arrangement in Atoms OBJECTIVES: Apply the aufbau principle, the Pauli exclusion principle, and Hund’s rule in writing the electron configurations of elements. Section 13.2 Electron Arrangement in Atoms OBJECTIVES: Explain why the electron configurations for some elements differ from those assigned using the aufbau principle. 7p 6d 7s 6p 5f 5d 6s 5p 4f 4d 5s Increasing energy 4p 4s 3d 3p 3s 2p 2s Aufbau diagram - page 367 1s Electron Configurations The way electrons are arranged in atoms. Aufbau principle- electrons enter the lowest energy first. This causes difficulties because of the overlap of orbitals of different energies. Pauli Exclusion Principle- at most 2 electrons per orbital - different spins Electron Configuration Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to. Let’s determine the electron configuration for Phosphorus Need to account for 15 electrons 7p 6d 7s 6p 5f 5d 6s 5p 4f 4d 5s Increasing energy 4p 4s 3d 3p The first two electrons 3s go into the 1s orbital 2p 2s Notice the opposite spins only 13 more to go... 1s 7p 6d 7s 6p 5f 5d 6s 5p 4f 4d 5s Increasing energy 4p 4s 3d 3p 3s 2p The next electrons 2s go into the 2s orbital only 11 more... 1s 7p 6d 7s 6p 5f 5d 6s 5p 4f 4d 5s Increasing energy 4p 4s 3d 3p 3s 2p • The next electrons go 2s into the 2p orbital • only 5 more... 1s 7p 6d 7s 6p 5f 5d 6s 5p 4f 4d 5s Increasing energy 4p 4s 3d 3p 3s 2p • The next electrons go 2s into the 3s orbital • only 3 more... 1s 7p 6d 7s 6p 5f 5d 6s 5p 4f 4d 5s Increasing energy 4p 4s 3d 3p • The last three electrons 3s go into the 3p orbitals. 2p • They each go into 2s separate shapes • 3 unpaired electrons 1s • = 1s22s22p63s23p3 Exceptional Electron Configurations Orbitals fill in order Lowest energy to higher energy. Adding electrons can change the energy of the orbital. Half filled orbitals have a lower energy. Makes them more stable. Changes the filling order Write these electron configurations Titanium - 22 electrons 1s22s22p63s23p64s23d2 Vanadium - 23 electrons 1s22s22p63s23p64s23d3 Chromium - 24 electrons 1s22s22p63s23p64s23d4 expected But this is wrong!! Chromium is actually: 1s22s22p63s23p64s13d5 Why? This gives us two half filled orbitals. Slightly lower in energy. The same principal applies to copper. Copper’s electron configuration Copper has 29 electrons so we expect: 1s22s22p63s23p64s23d9 But the actual configuration is: 1s22s22p63s23p64s13d10 This gives one filled orbital and one half filled orbital. Remember these exceptions: d4, d9 Section 13.3 Chemical Physics and the Quantum Mechanical Model OBJECTIVES: Calculate the wavelength, frequency, or energy of light, given two of these values. Section 13.3 Chemical Physics and the Quantum Mechanical Model OBJECTIVES: Explain the origin of the atomic emission spectrum of an element. Light The study of light led to the development of the quantum mechanical model. Light is a kind of electromagnetic radiation. Electromagnetic radiation includes many kinds of waves All move at 3.00 x 108 m/s = c Parts of a wave Crest Wavelength Amplitude Origin Trough Parts of Wave - p.372 Origin - the base line of the energy. Crest - high point on a wave Trough - Low point on a wave Amplitude - distance from origin to trough (-) or crest (+) Wavelength - distance from crest to crest Wavelength is abbreviated by the Greek letter lambda = l Frequency The number of waves that pass a given point per second. Units: cycles/sec or hertz (Hz or sec-1) Abbreviated by Greek letter nu = n c = ln Frequency and wavelength Are inversely related As one goes up the other goes down. Different frequencies of light are different colors of light. There are a wide variety of frequencies The whole range is called a spectrum, Fig. 13.10, page 373 Low High energy energy Radio Micro Infrared Ultra- X- Gamma waves waves . violet Rays Rays Low High Frequency Frequency Long Short Wavelength Wavelength Visible Light Prism White light is made up of all the colors of the visible spectrum. Passing it through a prism separates it. If the light is not white By heating a gas with electricity we can get it to give off colors. Passing this light through a prism does something different. Atomic Spectrum Each element gives off its own characteristic colors. Can be used to identify the atom. How we know what stars are made of. • These are called discontinuous spectra, or line spectra • unique to each element. • These are emission spectra • The light is emitted given off • Sample 13-2 p.375 Light is a Particle Energy is quantized. Light is energy Light must be quantized These smallest pieces of light are called photons. Photoelectric effect? Energy & frequency: directly related. Energy and frequency E =hxn E is the energy of the photon n is the frequency h is Planck’s constant h = 6.6262 x 10 -34 Joules x sec. joule is the metric unit of Energy The Math in Chapter 13 2 equations so far: c = ln E = hn Know these! Examples What is the wavelength of blue light with a frequency of 8.3 x 1015 hz? What is the frequency of red light with a wavelength of 4.2 x 10 -5 m? What is the energy of a photon of each of the above? Explanation of atomic spectra When we write electron configurations, we are writing the lowest energy. The energy level, and where the electron starts from, is called it’s ground state- the lowest energy level. Changing the energy Let’s look at a hydrogen atom Changing the energy Heat or electricity or light can move the electron up energy levels (“excited”) Changing the energy As the electron falls back to ground state, it gives the energy back as light Changing the energy May fall down in steps Each with a different energy Ultraviolet Visible Infrared Further they fall, more energy, higher frequency. This is simplified The orbitals also have different energies inside energy levels All the electrons can move around. What is light? Light is a particle - it comes in chunks. Light is a wave- we can measure its wavelength and it behaves as a wave 2 If we combine E=mc , c=ln, E = 1/2 mv2 and E = hn We can get: l = h/mv called de Broglie’s equation Calculates the wavelength of a particle. Sample problem What is the approximate mass of a particle having a wavelength of 10-7 meters, and a speed of 1 m/s? Use l = h/mv = 6.6 x 10-27 (Note: 1 J = N x m; 1 N = 1 kg x m/s2 Matter is a Wave Does not seem to apply to large objects Things bigger than an atom A baseball has a wavelength of about 10-32 m when moving 30 m/s Anelectron at the same speed has a wavelength of 10-3 cm Big enough to measure. The chemical physics of the very small Quantum mechanics explains how the very small behaves. Classic physics is what you get when you add up the effects of millions of packages. Quantum mechanics is based on probability Heisenberg Uncertainty Principle Itis impossible to know exactly the location and velocity of a particle. The better we know one, the less we know the other. Measuring changes the properties. Instead, analyze interactions with other particles More obvious observations with the very small To measure where a electron is, we use light. But the light moves the electron And hitting the electron changes the frequency of the light. Before After Photon Photon changes wavelength Moving Electron Electron Changes velocity Fig. 13.19, p. 382