* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Energy, Heat, and Work* Oh My*
Canonical quantization wikipedia , lookup
EPR paradox wikipedia , lookup
Wave function wikipedia , lookup
Quantum key distribution wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Renormalization group wikipedia , lookup
Quantum state wikipedia , lookup
Renormalization wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Molecular orbital wikipedia , lookup
Double-slit experiment wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Mössbauer spectroscopy wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Matter wave wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Particle in a box wikipedia , lookup
Tight binding wikipedia , lookup
Wave–particle duality wikipedia , lookup
Probability amplitude wikipedia , lookup
Electron scattering wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Atomic theory wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron configuration wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Alcatraz is Closed (1963) Reading for Wednesday HOMEWORK – DUE Wednesday 3/22/17 EXP 10 Lab Wednesday/Thursday WS 12 (Worksheet): (from course website) CH 7 EC: 5, 7, 8, 9, 11, 12, 14, 15, 20, 21, 24, 29, 30, 31, 34, 39, 50, 51, 52, 55-59 all, 64, 69, 71, 72, 90 Lab Today/Tomorrow WS 11 (Worksheet): (from course website) HOMEWORK – DUE Monday 3/27/17 Chapter 8 sections 1-2 Open office hours Exam 3 NEXT Monday Spectra When atoms or molecules absorb energy, that energy is often released as light energy fireworks, neon lights, etc. When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum non-continuous can be used to identify the material Examples of Spectra The Bohr Model of the Atom The energy of the atom is quantized, and the amount of energy in the atom is related to the electron’s position quantized means that the atom could only have very specific amounts of energy The electron’s positions within the atom (energy levels) are called stationary states Each state is associated with a fixed circular orbit of the electron around the nucleus. The higher the energy level, the farther the orbit is from the nucleus. The The first orbit, the lowest energy state, is called the ground state. atom changes to another stationary state only by absorbing or emitting a photon. Photon energy (hn) equals the difference between two energy states. The Bohr Model of the Atom - 5 4 3 2 1 nucleus - - Emission Spectra Bohr Model of H Atoms Emission Spectra Hydrogen Energy Transitions Which is a higher energy transition? 65 or 32 6 5 53 or 31 23 or 34 4 3 2 1 nucleus Rydberg’s Spectrum Analysis Rydberg developed an equation involved an inverse square of integers that could describe the spectrum of hydrogen. 1 1 R 2 2 n n 1 2 1 1.096776 107 R m What is the wavelength (nm) of light based on an electron transition from n = 4 to n = 2? 1.0968 107 m 1 1 1 2 2 2 4 1 2056875 m HUH?!?!? 486 nm Wave Behavior of Electrons de Broglie proposed that particles could have wave-like character Predicted that the wavelength of a particle was inversely proportional to its momentum Because an electron is so small, its wave character is significant hc E= hc h h 2 = mc = λ= mc mv 2 E = mc h = planks constant Js kg m 2 s2 s m = mass of particle kg v = velocity m s What is the wavelength of an electron traveling at 2.65 x 106 m/s. (mass e- = 9.109x10-31 kg) h λ= mv λ= 2 34 kg m 6.626 10 s 31 9.109 10 kg 2.65 106 m s 2.745 1010 m Determine your wavelength if you are walking at a pace of 2.68 m/s. (1 kg = 2.20 lb) λ= 2 34 kg m 6.626 10 s 91.8 kg 2.68 ms 2.96 1036 m The Quantum Mechanical Model of the Atom The matter-wave of the electron occupies the space near the nucleus and is continuously influenced by it. The Schrödinger wave equation allows us to solve for the energy states associated with a particular atomic orbital. h2 8 me 2 2 2 2 2 2 y z x V x, y, z Ψ x, y, z EΨ HΨ EΨ The square of the wave function (Y2) gives the probability density, a measure of the probability of finding an electron of a particular energy in a particular region of the atom. Probability & Radial Distribution Functions y2 is the probability density The Radial Distribution function represents the total probability at a certain distance from the nucleus the probability of finding an electron at a particular point in space decreases as you move away from the nucleus maximum at most probable radius Nodes in the functions are where the probability drops to 0 Probability Density Function The probability density function represents the total probability of finding an electron at a particular point in space Radial Distribution Function The radial distribution function represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases The net result is a plot that indicates the most probable distance of the electron in a 1s orbital of H is 52.9 pm 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 These integers are called quantum numbers principal quantum number, n angular momentum quantum number, l magnetic quantum number, ml Principal Quantum Number, n Characterizes the energy of the electron in a particular orbital and the size of that orbital n can be any integer 1 The larger the value of n, the more energy the orbital has The larger the value of n, the larger the orbital corresponds to Bohr’s energy level Greater relative distance from the nucleus As n gets larger, the amount of energy between orbitals gets smaller Energies are defined as being negative an electron would have E = 0 when it just escapes the atom Principal Quantum Number, n The energies of individual energy levels in the hydrogen atom (and therefore the energy changes between levels) can be calculated. En hcR 1 n2 1 1 E hcR 2 2 n final ninitial What is the energy of a photon of light based on an electron transition from n = 4 to n = 2? 34 19 7 8m 2.180 6.62610 1018 JJ s 2.998 1 1 10 4.087 1.0968 1010 J 1 1 EE44 2 2 2 2 22 2 photon photon photon m 4s 4 2 Principal Energy Levels in Hydrogen Angular Momentum Quantum Number, l The angular momentum quantum number determines the shape of the orbital l can have integer values from 0 to (n – 1) Each l is called by a particular letter that designates the shape of the orbital s (spherical) orbitals are spherical p (principal) orbitals are like two balloons tied at the knots d (diffuse) orbitals are mainly like four balloons tied at the knot f (fundamental) orbitals are mainly like eight balloons tied at the knot principal (n) quantum number 1 2 3 4 5 possible angular momentum (l) quantum number(s) 0 (s) 0, 1 (s, p) 0, 1, 2 (s, p, d) 0, 1, 2, 3 (s, p, d, f) 0, 1, 2, 3, 4 (s, p, d, f, g) Magnetic Quantum Number, ml The magnetic quantum number is an integer that specifies the orientation of the orbital Values are integers from −l to +l the direction in space the orbital is aligned relative to the other orbitals including zero Gives the number of orbitals of a particular shape l = 2, the values of ml are −2, −1, 0, +1, +2; which means there are five orbitals with l = 2 when