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Arrangement of Electrons in Atoms 4-1 The Development of a New Atomic Model The Development of a New Atomic Model How do electrons surround the nucleus of the atom? “The emission of light is fundamentally related to the behavior of electrons.” Properties of Light Scientists early in the 1900’s believed that light behaved like a wave. Light also behaves like a particle. Confused? We’ll discuss this later… Electromagnetic Radiation – a form of energy that exhibits wavelike behavior as it travels through space. Properties of Light Electromagnetic Spectrum – all the forms of electromagnetic radiation. Fig. 4-1 on pg. 92. * You need to know all these forms of light, including approximate wavelength and frequency. Properties of Light All these forms of light have the same speed. c = 3 x 108 m/s Speed of light in a vacuum. Speed of light in other mediums is more. Properties of a Wave: Wavelength () – the distance between corresponding points on adjacent waves. Wavelength values can be very small or very large. Red light = 700 nm Radio wave = 100 m 1 nm = 1 x 10-9 m Properties of a Wave: Frequency () – the number of waves that pass a given point in a specific time, usually 1 second. Unit is wave/second. * 1 wave/second = 1 hertz (Hz) Fig. 4-2 pg. 92 Properties of a Wave: Amplitude – is the height of the wave measured from the origin to its crest. The brightness or intensity of the light depends on the amplitude. The greater the amplitude, the brighter the light. Properties of a Wave: Important Equation #1: c = Speed of Light = wavelength x frequency is inversely proportional to As increases decreases. As decreases increases. Photoelectric Effect Refers to the emission of electrons from a metal when light shines on the metal. The photoelectric effect explains phenomenon such as solar powered calculators, automatic street lights, automatic doors, … Photoelectric Effect For a given metal, no electrons were emitted if the lights frequency was below a certain minimum. The brightness of a light won’t necessarily cause electrons to flow. Ex. Red light will not cause electrons to flow in a sheet of sodium metal, no matter how long or bright the source is. Violet light will cause electrons to flow. Violet light has a greater frequency, and a greater amount of energy per photon. Photon? Different metals require different amounts of energy depending on how tightly the electrons are bound to the metal. Light as Particles Max Planck said an object emits energy in small amounts called quanta. Quantum – the minimum quantity of energy that can be lost or gained by an atom. Follow closely now, this is weird. Planck’s Theory Max Planck predicted accurately how the spectrum of radiation emitted by an object changes with temperature. Light as Particles Energies absorbed or emitted by atoms are quantized, which means that their values are restricted to certain quantities. Energy is not continuous. Ramps vs. Stairs = Continuous vs. Quantized Ex. Imagine a car’s fundamental quantum of energy corresponds to a speed of 10 km/hr. If the car has 7 quanta of energy, it will have a speed of 70 km/hr. If the car has 9 quanta of energy, it will have a speed of 90 km/hr. This shows that a car can only move in multiples of 10 km/hr (in this case). Speeds such as 88 km/hr and 41 km/hr are impossible. Light as Particles Quantized Continuous Light as Particles Important Equation #2: E = h Planck’s Constant (h) = 6.6262 x 10-34 Js (Joule x seconds) Einstein showed their was a wave-particle duality (meaning wave and particle) The Hydrogen-Atom LineEmission Spectrum Ground State – the lowest energy state of an atom Excited State – state at which an atom has a higher potential energy than its ground state. See fig. 4-8 on pg. 96 The Hydrogen-Atom LineEmission Spectrum When an excited electron returns to the ground state, it gives off energy in the form of electromagnetic radiation. The energy of a photon is equal to the difference in energy between the atom’s initial state and its final state. See fig. 4-5, 4-6 and 4-7 on pg. 95 The Hydrogen-Atom LineEmission Spectrum Bohr Model of the Hydrogen Atom According to the Bohr’s Model, electrons orbit the nucleus in allowed paths, called orbits. Similar to planets orbiting the sun. According to this model, electrons cannot exist between energy levels. Bohr Model of the Hydrogen Atom The farther the electron is from the nucleus, the more energy it possesses. I’ll explain line-spectrum’s more in class. Bohr’s Model is OK, but it isn’t complete. It is only good for explaining the hydrogen atom, not multielectron atoms. Arrangement of Electrons in Atoms 4-2 The Quantum Model of the Atom Electrons as Waves Last section we learned that light can behave as both a particle and a wave. What about electrons? Louis De Broglie stated that electrons could be considered waves confined to a space around an atomic nucleus. Electron waves can exist, but only at specific frequencies corresponding to specific frequencies. Electrons as Waves Experiments showed that electrons (like light) could be bent, or diffracted. Also, electron beams could interfere with each other. Diffraction – bending of light when passed through a crystal. Interference – overlapping of waves, reducing energy in some areas. Heisenberg Uncertainty Principle The position and momentum of a moving object can not simultaneously be measured and known exactly. Due to the duel nature of matter and energy Only important with small scale objects The Schrödinger Wave Equation Erwin Schrödinger developed an equation, which treated electrons in atoms as waves. Solutions to wave equation are known as wave functions. Don’t worry about wave functions, we do a little more with it in AP Coupled with Heisenberg Uncertainty Theory, lead to Quantum Theory Quantum Theory – describes mathematically the wave properties of electrons and other very small particles. The Schrödinger Wave Equation Most Important Idea: We can only know the probability of finding an electron, not its exact location. Orbital – a 3-dimensional region around the nucleus that indicates the probable location of an electron. Fig 4-11 Review Energy is quantized ( found in specific amounts) Electrons have wavelike behavior Impossible to know electron position and momentum. Can predict the probability of electron location Called the Quantum-mechanical model Probability and Orbital The density of an electron cloud is called the electron density. Higher density – more likely to find electron Lower density – less likely to find electron An orbital is the region where a given electron is likely found. There are different types of orbitals….s, p, d, f which we will talk about more later. Orbitals and Energy To describe orbitals, scientists use quantum numbers. Quantum Number – specify the properties of atomic orbitals and the properties of electrons in orbitals. Principal Quantum Number indicates the main energy level occupied by the electron. Sometimes considered the shell. n are positive integers (n = 1, n=2, n=3, …) As n increases, energy and distance from nucleus increases. n = 1 is the lowest energy level, closest to the nucleus. More than one electron can have the same value of n. The total number of orbitals that exist in a given shell is equal to n2. Angular Momentum Quantum Number (l) indicates the shape of an orbital Also considered the sublevel. The number of orbital shapes possible is equal to n l can have values of 0 and all positive integers less than or equal to n-1 If n = 1, l = 0: (l = n – 1 = 1 –1 = 0) If n = 2, l = 1 and 0: (l = n – 1 = 2 – 1 = 1) Each orbital is assigned a letter, which corresponds to a shape s orbital – see figure 4-25 pg 144 p orbital- see figure 4-26 in book d orbital – see figure 4-27 in book Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel. Ex. 1s sublevel is the s orbital is in the first main energy level Ex. 2p sublevel is the set of p orbitals in the second energy level Ex. 3d sublevel is the set of d orbitals in the third energy level Magnetic Quantum Number (ml ) indicates the orientation of an orbital around the nucleus ml = +/- l and every integer in between Ex. If n = 1, l = 0, ml = 0 This means there is a single s orbital in the first energy level If n = 2, l = 1, ml = -1, 0, +1 In the second energy level there are three p orbitals If n = 4, l = 2, ml = -2, -1, 0, +1, +2 In the fourth energy level there are five d orbitals. If n = 4, l = 0, ml = 0 In the fourth energy level there is 1 s orbital Spin Quantum Number (ms) indicates the spin states of an electron in an orbital, either +1/2, or –1/2. o Electrons spin on an internal axis either clockwise or counterclockwise. A single orbital can hold a maximum of two electrons, which must have opposite spins. Summary of Energy Levels, Sublevels, and Orbitals Principal Energy Level n=1 Sublevels Orbitals 1s 1s (one) n=2 2s, 2p 2s (one) + 2p (three) n=3 3s, 3p, 3d 3s(one) + 3p(three)+3d(five) n=4 4s, 4p, 4d, 4f 4s(one)+4p(three)+4d(five)+ 4f(seven) Max Number of Electrons in Each Sublevel Sublevel # of Orbitals s 1 Max # of Electrons 2 p 3 6 d 5 10 f 7 14 Arrangement of Electrons in Atoms 4-3 Electron Configurations Electron Configuration Describes where the electrons are found and what energies they possess. They are determined by distributing the atoms electrons among levels, sublevels, and orbitals based on a set of principles. Determining Electron Configurations They fill using the Aufbau Principle Electrons in atoms want to assume the lowest possible energy. Ground-state electron configuration Order Orbitals are filled * Note 4sfills before 3d, this is what is found in nature. The energy levels get closer together farther from nucleus. Pauli Exclusion Pauli Exclusion Principle An orbital can hold a maximum of 2 electrons. 2 electrons in the same orbital must have opposite spins. An electron is "paired" if it is sharing an orbital with another electron with an opposite spin. An electron is "unpaired" if it is alone in an orbital Hunds Rule Electrons occupy equal-energy orbitals so that a maximum number of unpaired electrons results. You must put a single electron in each equal-energy orbital before you begin to pair. Short Cut to remembering order….either one works Sample 1 Sample 2 You try Write the configurations for A) magnesium and B) Nickel. How many unpaired electrons does each possess? A) Mg: 1s22s22p63s2 No unpaired B) Ni: 1s22s22p63s23p64s23d8 Two Unpaired We will learn this chart later