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October 16, 2014 October 16, 2014 Chapter 5: Electrons in Atoms Honors Chemistry Bohr Model Niels Bohr, a young Danish physicist and a student of Rutherford improved Rutherford's model. Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus. Each electron orbit has a fixed energy. Energy levels: the fixed energies of an electron. Quantum: The amount of energy required to move an electron from one energy level to another level. Light Electrons can jump from one energy level to another. The term quantum leap can be used to describe an The modern quantum model grew out of the study of light. 1. Light as a wave abrupt change in energy. 2. Light as a particle -Newton was the first to try to explain the behavior of light by assuming that light consists of particles. October 16, 2014 Light as a Wave 1. Wavelength-shortest distance between equivalent points on a continuous wave. symbol: λ (Greek letter lambda) 2. Frequency- the number of waves that pass a point per second. symbol: ν (Greek letter nu) 3. Amplitude-wave's height from the origin to the crest or trough. 4. Speed-all EM waves travel at the speed of light. symbol: c=3.00 x 108 m/s in a vacuum The speed of light Calculate the following: 8 1. The wavelength of radiation with a frequency of 1.50 x 1013 c=3.00 x 10 m/s Hz. Does this radiation have a longer or shorter wavelength than red light? (2.00 x 10-5 m; longer than red) c=λν 2. The frequency of radiation with a wavelength of 5.00 x 10-8 m. The wavelength and frequency are inversely proportional In which region of the electromagnetic spectrum is this radiation? to each other. (6.00 x 1015 Hz; ultraviolet) Electromagnetic Radiation light consists of electromagnetic waves. This radiation includes Light as a Particle radio waves, microwaves, infrared waves, visible light, • Einstein ultraviolet waves, X-rays, and gamma rays. > Light as a photon http://www.youtube.com/watch?v=cfXzwh3KadE > Photoelectric Effect Photoelectric Effect: refers to the emission of electrons from a metal when light shines on the metal.The photoelectric effect causes electrons to be ejected from the surface of a metal when light is of high enough frequency to hit the metal's surface. October 16, 2014 Light as a Particle E=hv • Wave behavior of light cannot explain why heated objects give off distinct colors (specific frequencies) of light. Planck proposed the previous relationship between a quantum of energy and the frequency of radiation. • Max Planck (1858-1947) > studied the different wavelengths of light emitted by E= energy, in joules heated objects v= frequency in s-1 > conclusion: matter can gain or lose energy only in h= Planck's constant 6.626 x 10-34 J·s specific amounts. • quantum-minimum energy that can be gained or lost by an atom E=hc > hot objects emit light in quantized amounts λ http://www.youtube.com/watch?v=Xmq_FJd1oUQ Practice Physics and the Quantum Mechanical Model The yellow vapor from a sodium lamp emits 3.37 x 10-19 J. Wave-Particle Duality What is the wavelength of this light? E=hv E=hc λ 3.37x 10-19 J=(6.626 x 10-34 Js)(3.00x 108 m/s2) λ λ= 5.89 x 10-7 m or 589 nm October 16, 2014 Atomic Spectra When atoms absorb energy, electrons move into higher energy levels. These electrons then lose energy by emitting light when they return to lower energy levels. Atomic emission spectrum: the frequencies of light that are emitted by an element into separate discrete lines. The fact that hydrogen atoms emit only specific frequencies of light indicated that the energy differences between the atoms' energy states were fixed. The following figure is the line-emission spectrum for hydrogen. Explanation of the Atomic Emission Spectra Bohr's model not only explained why the emission spectrum of hydrogen consists of specific frequencies of light, but it also predicted specific values of these frequencies. Ground State: When an electron has its lowest possible energy. The principal quantum number (n) is 1. *If the electron is then excited to a higher energy level, the dropping of the electron to a lower energy level creates the light emitted. October 16, 2014 Quantum Mechanical Model Quantum Mechanical Model de Broglie's Hypothesis • matter has wave-like properties • consequence: whole number of wavelengths must fit within the circumference of the orbit. • The energy level number, n, is equal to the number of waves. Heisenberg uncertainty principle: It is impossible to know exactly both the velocity and the position of a particle at the same time. We define electron energy exactly but accept that we do not know the electrons definite position. Impossible to take any measurement of an object without disturbing it! Quantum Mechanical Model http://www.youtube.com/watch?v=7SjFJImg2Z8&feature=player_embedded Quantum Mechanical Model http://www.youtube.com/watch?v=uWMTOrux0LM Erwin Schrödinger used results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. *The quantum mechanical model determines the allowed energies of an electron and how likely it is to find the electron in various locations around the nucleus. Probability of finding a hydrogen electron. We can apply to other elements. October 16, 2014 Orbit vs. Orbital Orbit: defined path of an electron (Bohr) Orbital: defined area of space for finding an electron. (Schrodinger) Types of Orbitals • The most probable area to find these electrons take on a shape. • So far, we have 4 shapes. > s, p, d, f. • No more than 2 electrons assigned to an orbital. > One spins clockwise, one spins counterclockwise. October 16, 2014 Atomic Orbitals and Quantum Numbers Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals. This first three quantum numbers result from the Schrödinger equation. Quantum Number Definition Symbol n principle quantum number angular momentum quantum number l (shape of the orbital) magnetic quantum number m l (orientation) m s spin quantum number Principal Quantum Number (n) Angular Momentum Quantum Number (l) Indicates the shape of the orbital. Indicates the main energy level occupied by the electron. n= 1, 2, 3 and so on. The number of orbital shapes possible is equal to n. As n increases, the electron's energy and its average distance from the nucleus increases. l=n-1 *The total number of orbitals that exist in a given shell L value Letter/Shape Ex: If n=2; L has two sublevels, 0 s the s and p orbitals because 1 p l=n-1; l=0 and 1 2 d How many sublevels would n=3 have? _________ 3 f October 16, 2014 Magnetic Quantum Number (ml) Spin Quantum Number (ms) Indicates the orientation of an orbital around the nucleus. Only two possible values (+1/2 and -1/2) which indicate the Values of m are whole numbers; 0 from L to -L two fundamental spin states of an electron in an orbital. m=-L...0...L A single orbital can then hold how many electrons? ______ Because an s orbital is spherical and is centered around the nucleus, it has only one possible orientation. How many orientations are present in the following orbitals? Tying all Quantum Numbers Together We can combine all four quantum numbers together to give us 1 atomic orbital contains 2 electrons. p orbitals ___________ Depending on the subshell, there may be different number of atomic orbitals present. The combination of the quantum numbers will tell us whether we are talking about an entire subshell or one atomic orbital. d orbitals ___________ *This may seem confusing until we do an example f orbitals ___________ Tying all Quantum Numbers Together Table of Allowed Quantum Numbers n=1, L= 0, ml=0, ms= +1/2, -1/2 This is one atomic orbital n l m ms 2 If I asked you to write all of the allowed quantum number combinations for n=3, this would be all quantum numbers for the n=3 subshell. October 16, 2014 1. Aufbau Principle Electron Configuration Electrons occupy the orbitals of lowest energy first. Introduction Definition The ways in which electrons are arranged in various orbitals around the nuclei of atoms. Change proceeds toward the lowest possible energy. 3 Rules: These three rules tell you how to find the electron configurations of atoms. 1. Aufbau principle 2. Pauli Exclusion Principle 3. Hund's Rule 2. Pauli Exclusion Principle 3. Hund's Rule electrons occupy orbitals of the same energy in a way that makes the an atomic orbital may describe at most two electrons. number or electrons with the same spin direction as large as possible. *To occupy the same orbital, two electrons must have opposite spins. October 16, 2014 Orbital Notation vs. Electron-Configuration Notation What element is represented by the following orbital diagram? Orbital Notation: an unoccupied orbital is represented by a line, ___, with the orbital's name written underneath the line. An orbital How many unpaired electrons are present? containing one electron is represented as ____. A orbital containing two electrons is represented as ____. Electron-Configuration Notation: Eliminates the lines and arrows. Instead, the number of electrons in a sublevel is shown by adding a superscript to 1s2 2s2 2p6 3s1 the sublevel. Ex: Hydrogen is represented by 1s1 Example: H, He, Li, Be, B Sample Problem Steps for Writing Electron Configurations 1. Locate the element on the periodic table. The electron configuration of boron is 1s22s22p1.
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