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Electrons in Atoms and The Quantum Theory Unit III Ch. 5 Warm Up-02/06/13 Define isotope. 2. How do you calculate the number of neutrons in an atom? 3. What does an atom’s atomic mass tell you? 4. What can you never change about an atom? 1. Warm Up-02/12/13 1. 2. 3. What does Pauli’s Exclusion Principle tell you about how electrons enter their orbitals? What does Hund’s Rule tell you about how electrons enter their orbitals? What does the Aufbau Principle tell you about how electrons enter their orbitals? Warm Up Please complete a K-W-L chart concerning electron configuration. 1. 2. 3. What do I know about electron configurations? What would I like to know about electron configurations? What did I learn about electron configurations (after class)? Warm Up-02/08/13 1. 2. 3. 4. 5. How many electrons will fit in the “s” suborbital? How many electrons will fit in the “p” suborbital? How many electrons will fit in the “d” suborbital? How many electrons will fit in the “f” suborbital? Please draw electron configurations for the following: He, Na, Mg, Zn and Br. Homework: Chapter 3 Due Date: 02/13/13 Page 137: 18-22. Page 146: 46-52, omit 51 Page 147: 77-80 Warm Up 1. 2. 3. 4. 5. Construct the iron. Construct the silicon. Construct the potassium. Construct the titanium. Construct the cobalt. electron configuration for electron configuration for electron configuration for electron configuration for electron configuration for Warm Up 1. 2. 3. 4. What percent are carbon and oxygen in CO2? What percent are calcium, sulfur and oxygen in CaSO4? What percent are sodium, nitrogen and oxygen in NaNO3? What percent are calcium and clorine in CaCl2? Electromagnetic Energy Frequency (); measured in units of hertz (sec-1) Wavelength () - measured units of length: mm, nm Amplitude - the height of the wave Speed (velocity) of electromagnetic energy = 3.00 x 108 m/s c= Electromagnetic Spectrum Wavelength () 1-800 m 10-1 - 10-2 m 10-2 - 10-4 m 10-4 - 10-6 m 400-700 nm 10-8 - 10-10 m 10-10 - 10-13 m 10-13 - 10-15 m Description Radio waves Radar Microwaves Infrared Visible Ultraviolet X-rays Gamma Rays Frequency () 104 - 109 109 - 1010 1010 - 1012 1012 - 1014 1014 - 1015 1015 - 1018 1018 - 1021 1021 - 1023 Spectroscopy The method of studying substances exposed to some sort of exciting energy. Spectrum Observed when white light is dispersed into the colors of the rainbow by a prism or diffraction grating. Emission Spectra Absorption Spectra The Photoelectric Effect The emission of electrons from a metal when light shines upon it. If the light frequency was below a certain level, no electrons were emitted. The wave theory of light predicted that light of any frequency could supply enough energy to eject an electron. Scientists could not explain why a certain minimum frequency was required. Radiation Caused by an unstable nucleus which will eject either a particle or energy until it reaches a more stable arrangement. Emission Description alpha helium nucleus beta high speed electron gamma v. high energy X-rays Planck’s Hypothesis In 1900 Max Planck was studying black body radiation. He suggested that hot objects emit energy in small specific amount called quanta. A quantum is the minimum amount of energy that can be gained or lost by an atom. Energy is given off (emitted) in little packets (or quanta) called photons. The amount of energy emitted is proportional to the frequency of the light emitted according to the equation: E = hn E = energy of a quantum or radiation n = the frequency of the radiation h = 6.626 x 10-34 J · s (h = Planck’s constant) Einstein (1905) introduced the concept that electromagnetic radiation has a dual waveparticle nature. Relationship between electromagnetic energy and electrons An electromagnetic wave of a certain frequency has only one possible wavelength: = c/n It has only one possible amount of energy: E = hn c and h are constants. If frequency, wavelength or energy is known, we can calculate the other two. White light can be thought of as a wave or as a stream of particles, which Einstein called photons. A photon is a particle of radiation having zero rest mass and carries a quantum of energy. Therefore, Ephoton = hn The Hydrogen Atom Line-Emission Spectrum See p. 127 for an explanation of ground state and excited state for an atom. Ground state - The smallest orbit an electron can occupy. The energy of the photon, Ephoton , corresponds to the energy difference between the different energy levels in an atom [ E1 and E2 , for example]. Rutherford-Bohr Atom This is referred to as the Planetary Atomic Model because they proposed that the negatively-charged electrons stay "in orbit" around the positively-charged nucleus in the same way that the planets stay in orbit around the sun. The Quantum Theory and the Hydrogen Atom Energy is given off in quanta. Bohr pointed out that the absorption of light by hydrogen at definite wavelengths corresponds to definite changes in the energy of the electron. He concluded that the orbits must have orbits of definite diameter. Mechanics Newtonian Mechanics - describes visible objects at ordinary velocities. Quantum Mechanics - describes extremely small particles at velocities near that of light Modern Atomic Structure E = mc2 E = h mc2 = h mv2 = h mv2 = hv/ = hv/mv2 = h/mv momentum = mv = p = h/p Heisenberg (1927) Heisenberg Uncertainty Principle It is not possible to know precisely the position of an electron and its momentum (velocity) at the same instant. Schrödinger Developed a mathematical equation to describe the wave-like behavior of the electron. The equation is very complicated (using second partial derivatives) is the wave function. The equation related the amplitude of the wave function () to any point in space around the nucleus. Max Born showed that ||2 gives the probability of finding the electron at the point in space for which the equation was solved. Einstein Proposed that electromagnetic radiation can be viewed as a steam of “particles” called photons. The energy of each photon is given by: E = h = h(c/) E = mc2 “Energy has mass” m=E/c2 = (hc/)/c2 = h/c m=mass of a photon of light with a wavelength Conclusions Energy is quantized Electromagnetic radiation shows some characteristics of matter Light as a wave: (sine wave) Light as a stream of photons: Wave Mechanical Model of the Atom Bohr’s model was based on classical physics and was shown to be inadequate. Mid-1920’s: a new approach was taken by de Bröglie, Heisenberg and Schrödinger. De Bröglie proposed that the electron, which had been considered a particle only, also showed wave properties. Schrödinger attacked the problem by putting emphasis on the wave properties. Atomic Orbitals & Quantum Numbers The quantum theory describes the behavior of electrons. There are four quantum numbers which are needed to describe the electron in an atom (n, l, m, s). Remember, no two electrons in an atom can have the same four quantum numbers. n, The Principal Quantum Number represents the main energy level, its "size". Can have values of 1, 2, 3, 4, … l, Angular Momentum Quantum Number, describes the "shape" of the orbital. These are multiple energy states that are grouped very close together. Can have values from 0 to n-1. The number of sublevels for energy level "n" = n n = 1 » 1 sublevel n = 2 » 2 sublevels n = 3 » 3 sublevels n = 4 » 4 sublevels m, Magnetic Quantum Number, describes the orientation (direction) of the orbital in space; that is, the direction in which it points. Can have values from -l to +l Degenerate orbitals are those orbitals with the same size (n) and shape (l) which have the same energy. the three 2p orbitals the five 3d orbitals s, Electron Spin Quantum Number. Electrons can spin either clockwise or counterclockwise. s can have one of two values depending on the direction of the rotation: +1/2 or -1/2 Quantum Number Overview n - principal quantum number - size of energy level values: 1, 2, 3, 4,… l - energy sublevel - shape of the orbital values: 0 to n-1 m - orbital Q.N. - orientation in space (direction) values: - l to + l s - spin Q.N. values: +1/2, -1/2 Rules for Filling Orbitals Aufbau Principle - Build up the electrons from the bottom Pauli Exclusion Principle - No two electrons can have the same set of four (4) quantum numbers. Hund's Rule - Add one electron to each orbital of degenerate orbitals until all orbitals have at least one electron. Then start pairing up the remaining electrons. The Apparent Contradiction Waves can act as particles, and particles can act as waves Bohr’s atomic model explained light in terms of particle properties. Electrons (like light) have properties of both waves and particles Wave-particle duality of nature applies to all waves and all particles Electron Configuration When we write the electron configuration for a specific atom, we must specify the energy level (principal quantum number, 1,2,3,...), the sublevel (angular momentum quantum number, s, p, d, f) and the number of electrons in each sublevel (indicated via a superscript). Electron Configuration For example, the electron configuration for magnesium (which has 12 electrons) is: 1s22s22p63s2 When you add up all the exponents, you should get the total number of electron for that particular atom (in this case, 2 + 2 + 6 + 2 = 12) Modern Atomic Structure 1. The division between matter and energy is becoming even less clear. 2. de Bröglie Hypothesis (1923) led the way to the present theory of atomic structure. Electron Dot Diagrams >>>Rules <<< The elemental symbol represents the nucleus and all electrons not in the outer shell Write out the electron configuration (1s22s2…) selecting those electrons in the outer energy level only Each side represents an orbital. Draw dots to represent electrons in that orbital Quantum Theory The quantum theory describes the behavior of the electrons. There are four quantum numbers needed to describe the electron in an electron (n, l, m, s) No two electrons can have the same four quantum numbers Principal Quantum Number, n Represents the “size” of the energy level (orbital) Energy Sublevels, l Describes the “shape” of the orbital These are multiple energy states that are grouped very close together The number of sublevels (for each level) = n n=1 1 sublevel n=2 2 sublevels n=3 3 sublevels n=4 4 sublevels Orbital Quantum Number, m Describes the orientation of the orbital in space; the direction in which it points. Degenerate orbitals: those orbitals with the same size (n) and shape (l) which have the same energy. e.g., the three 2p orbitals the five 3d orbitals Electron Spin Quantum Number, s Electrons can spin either clockwise or counterclockwise “s” will have one of two values depending on the direction of rotation: +1/2 or -1/2 Distribution of Electrons How are electrons distributed among the energy levels? In a neutral atom: #e-’s = # protons = atomic no. Electrons always fill the energy level and sublevel to produce the lowest energy arrangement No two electrons can have the same 4 quantum numbers (Pauli Exclusion Principle) The max. no. of e in energy level “n” = 2n2 Aufbau Principle Build up the electrons from the bottom “The Aufbau Hotel” Hund’s Rule Add one electron to each orbital of degenerate orbitals until all orbitals have at least one electron. Then start pairing up the remaining electrons. Pauli Exclusion Principle No two electrons can have the same set of four (4) quantum numbers Heisenberg Uncertainty Principle It is not possible to know precisely the position of an electron and its momentum (velocity) at the same instant.