* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 7 The Quantum- Mechanical Model of the Atom
Survey
Document related concepts
Particle in a box wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Double-slit experiment wikipedia , lookup
Tight binding wikipedia , lookup
Electron scattering wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Atomic orbital wikipedia , lookup
Matter wave wikipedia , lookup
Electron configuration wikipedia , lookup
Hydrogen atom wikipedia , lookup
Wave–particle duality wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Transcript
Chapter 7 Lecture Lecture Presentation Chapter 7 The QuantumMechanical Model of the Atom ----Revised by Wang Sherril Soman Grand Valley State University © 2014 Pearson Education, Inc. The Nature of Light: Its Wave Nature • Light: a form of electromagnetic radiation Composed of perpendicular oscillating waves, one for the electric field, and one for the magnetic field • All electromagnetic waves move through space at the same, constant speed. 3.00 × 108 m/s = the speed of light © 2014 Pearson Education, Inc. Speed of Energy Transmission © 2014 Pearson Education, Inc. Characterizing Waves • The amplitude is the height of the wave. – The amplitude is a measure of light intensity. The larger the amplitude, the brighter the light. crest trough © 2014 Pearson Education, Inc. Characterizing Waves • The wavelength (l) is a measure of the distance covered by the wave. Wavelength (l) © 2014 Pearson Education, Inc. Characterizing Waves • The frequency (n) is the number of waves (the number of cycles) that pass a point in a given period of time. – Units are hertz (Hz) or cycles/s = s−1 (1 Hz = 1 s−1). • The total energy is proportional to, the amplitude of the waves, and the frequency. © 2014 Pearson Education, Inc. The Relationship Between Wavelength and Frequency speed, m/s frequency, /s (or Hz) wavelength, m Example 7.1 Wavelength and Frequency Calculate the wavelength (in nm) of the red light emitted by a barcode scanner that has a frequency of 4.62 × 1014 s–1. © 2014 Pearson Education, Inc. Color • The color of light is determined by its wavelength or frequency. • White light is a mixture of all the colors of visible light. – A spectrum – Red Orange Yellow Green Blue Indigo Violet • When an object absorbs some of the wavelengths of white light and reflects others, it appears colored. The observed color is predominantly the colors reflected. © 2014 Pearson Education, Inc. Amplitude and Wavelength © 2014 Pearson Education, Inc. The Electromagnetic Spectrum • Visible light comprises only a small fraction of all the wavelengths of light, called the electromagnetic spectrum. © 2014 Pearson Education, Inc. Continuous Spectrum © 2014 Pearson Education, Inc. Thermal Imaging using Infrared Light © 2014 Pearson Education, Inc. Using High-Energy Radiation to Kill Cancer Cells During radiation therapy, a tumor is targeted from multiple directions in order to minimize the exposure of healthy cells, while maximizing the exposure of cancerous cells. © 2014 Pearson Education, Inc. Electromagnetic wave – particles or waves ? © 2014 Pearson Education, Inc. Electromagnetic wave – particles or waves ? © 2014 Pearson Education, Inc. Einstein’s Explanation • Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons. • The energy of a photon of light is directly proportional to its frequency. – Inversely proportional to its wavelength – The proportionality constant is called Planck’s Constant, (h), and has the value 6.626 × 10−34 J ∙ s. © 2014 Pearson Education, Inc. Einstein’s Explanation Example 7.2 Photon Energy A nitrogen gas laser pulse with a wavelength of 337 nm contains 3.83 mJ of energy. How many photons does it contain? © 2014 Pearson Education, Inc. Spectra • When atoms or molecules absorb energy, that energy is often released as light energy, – Fireworks, n – eon lights, etc. Na © 2014 Pearson Education, Inc. K Li Ba Emission Spectra © 2014 Pearson Education, Inc. Indication of energy level of electrons Electrons in atoms are at discrete energy levels. The energy difference between the high level and the low level equals to the emitted photon energy. © 2014 Pearson Education, Inc. Rydberg’s Spectrum Analysis Johannes Rydberg (1854–1919) • Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers. © 2014 Pearson Education, Inc. Rutherford’s Nuclear Model • The atom contains a tiny dense center called the nucleus. • The nucleus is essentially the entire mass of the atom. • The nucleus is positively charged . • The electrons move around in the empty space of the atom surrounding the nucleus. © 2014 Pearson Education, Inc. Problems with Rutherford’s Nuclear Model of the Atom • Electrons are moving charged particles. • According to classical physics, moving charged particles give off energy. • Therefore, electrons should constantly be giving off energy. – This should cause the atom to glow! • The electrons should lose energy, crash into the nucleus, and the atom should collapse! – But it doesn’t! © 2014 Pearson Education, Inc. The Bohr Model of the Atom Neils Bohr (1885–1962) • Bohr’s major idea was that the energy of the atom was quantized, and that the amount of energy in the atom was related to the electron’s position in the atom. – Quantized means that the atom could only have very specific amounts of energy. © 2014 Pearson Education, Inc. Bohr Model of H Atoms © 2014 Pearson Education, Inc. Bohr Model of H Atoms photonener gy E E final Einitial 1 1 hn 2.18 10 J 2 2 n n final initial 1 c 1 18 h 2.18 10 J 2 2 l n n initial final 18 © 2014 Pearson Education, Inc. Bohr Model of H Atoms © 2014 Pearson Education, Inc. Bohr Model of H Atoms © 2014 Pearson Education, Inc. Bohr Model of H Atoms Example 7.7 Wavelength of Light for a Transition in the Hydrogen Atom Determine the wavelength of light emitted when an electron in a hydrogen atom makes a transition from an orbital in n = 6 to an orbital in n = 5. photonener gy E Einitial E final hn 2.18 10 h c l 18 2.18 10 © 2014 Pearson Education, Inc. 1 1 J 2 2 n n final initial 18 1 1 J n 2 n 2 initial final Wave Behavior of Electrons Louis de Broglie (1892–1987) • de Broglie proposed that particles could have wavelike character. v, speed Electron Diffraction © 2014 Pearson Education, Inc. Uncertainty Principle • Heisenberg stated that the product of the uncertainties in both the position and speed of a particle was inversely proportional to its mass. – x = position, x = uncertainty in position – v = velocity, v = uncertainty in velocity – m = mass • This means that the more accurately you know the position of a small particle, such as an electron, the less you know about its speed, and vice versa. © 2014 Pearson Education, Inc. Schrödinger’s Equation • Schrödinger’s equation allows us to calculate the probability of finding an electron with a particular amount of energy at a particular location in the atom. • Solutions to Schrödinger’s equation produce many wave functions, Y. • A plot of distance versus Y 2 represents an orbital, a probability distribution map of a region where the electron is likely to be found. © 2014 Pearson Education, Inc. Solutions to the Wave Function, Y • Calculations show that the size, shape, and orientation in space of an orbital are determined to be three integer terms in the wave function. – Added to quantize the energy of the electron. • These integers are called quantum numbers. – Principal quantum number, n – Angular momentum quantum number, l – Magnetic quantum number, ml © 2014 Pearson Education, Inc. Principal Quantum Number, n • Characterizes the energy level of the electron in a particular orbital. – Corresponds to Bohr’s energy level • n can be any integer 1. • n is also called principal shell. © 2014 Pearson Education, Inc. Angular Momentum Quantum Number, l • The angular momentum quantum number determines the shape of the orbital. It is also called subshell. • l can have integer values from 0 to (n – 1). • Each value of l is called by a particular letter that designates the shape of the orbital. – – – – I =0, s, I =1, p, I =2, d, I =3, f. © 2014 Pearson Education, Inc. Energy Levels and Sublevels © 2014 Pearson Education, Inc. ? Energy Levels and Sublevels Example 7.5 Quantum Numbers I What are the quantum numbers and names (for example, 2s, 2p) of the orbitals in the n = 4 principal level? © 2014 Pearson Education, Inc. Magnetic Quantum Number, ml • The magnetic quantum number is an integer that specifies the orientation of the orbital. – The direction in space the orbital is aligned relative to the other orbitals • Values are integers from −l to +l – Including zero – Gives the number of orbitals of a particular shape • When l = 2, the values of ml are −2, −1, 0, +1, +2, which means there are five orbitals with l = 2. © 2014 Pearson Education, Inc. Magnetic Quantum Number, ml © 2014 Pearson Education, Inc. n, l, ml © 2014 Pearson Education, Inc. n, l, ml Example 7.6 Quantum Numbers II These sets of quantum numbers are each supposed to specify an orbital. One set, however, is erroneous. Which one and why? a.n = 3; l = 0; ml = 0 b. n = 2; l = 1; ml = –1 c. n = 1; l = 0; ml = 0 d. n = 4; l = 1; ml = –2 © 2014 Pearson Education, Inc. Describing an Orbital • Each set of n, l, and ml describes one orbital. • Orbitals with the same value of n are in the same principal energy level. – Also called the principal shell • Orbitals with the same values of n and l are said to be in the same sublevel. – Also called a subshell © 2014 Pearson Education, Inc. l = 0, the s Orbital © 2014 Pearson Education, Inc. l =1, p Orbitals © 2014 Pearson Education, Inc. l =2, d Orbitals © 2014 Pearson Education, Inc. l=3, f Orbitals © 2014 Pearson Education, Inc.