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Unit 4 – Quantum Mechanics Cartoon courtesy of NearingZero.net
Light and Energy Much of what we know about electrons comes from study of light –Light behaves as waves –Light also behaves as particles (photons)
Wave properties Light waves are part of the electromagnetic spectrum Can be characterized by 5 properties: –Amplitude –Wavelength –Frequency –Speed –Energy
c = C = speed of light, a constant (3.00 x 10 8 m/s) = frequency, in units of hertz (hz, /s, s -1 ) = wavelength, in meters Electromagnetic radiation propagates through space as a wave moving at the speed of light.
Calculating the color of light… Given that a beam of light has frequency of 6.0 x 10 14 /s what is the wavelength of this light? What color is it? –use p.129
E = h E = Energy, in units of Joules (kg·m 2 /s 2 ) h = Planck’s constant (6.63 x 10 -34 J·s) = frequency, in units of hertz (hz, /s, s -1 ) = frequency, in units of hertz (hz, /s, s -1 ) The energy (E ) of electromagnetic radiation is directly proportional to the frequency ( ) of the radiation. This is the energy of a photon of a particular frequency.
Long Wavelength = Low Frequency = Low ENERGY Short Wavelength = High Frequency = High ENERGY Wavelength Table
…produces all of the colors in a “continuous spectrum” Spectroscopic analysis of the visible spectrum… (such as seen from an incandescent light bulb)
…produces a “bright line” or “emission spectrum” Spectroscopic analysis of the hydrogen spectrum… (as given off by a hydrogen gas-filled fluorescent light bulb)
’ When they ‘fall’ back to their ’ ‘ground state’ they emit photons of light with distinct wavelengths, visible as bands on an ‘emission spectrum’ (not all are in the visible range). Electron transitions occur when electrons absorb energy in a ‘quantum jump’ to an ‘excited state’. VISIBLEJUMPS
The Bohr Model of the Atom Neils Bohr I pictured electrons orbiting the nucleus much like planets orbiting the sun. But it turns out they’re more like bees around a hive. WRONG!!!
Quantum Mechanical Model of the Atom Mathematical laws were used to identify the regions outside of the nucleus where electrons are most likely to be found. These laws are beyond the scope of this class… But here are two important examples:
Schrodinger Wave Equation probability Equation for probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger
Heisenberg Uncertainty Principle You can find out where the electron is, but not where it is going. OR… You can find out where the electron is going, but not where it is! “One cannot simultaneously determine both the position and momentum of an electron.” Werner Heisenberg
Electron Energy Level (Shell) Generally symbolized by n, it denotes the average distance of the electron from the nucleus. Number of electrons that can fit in a shell: 2n 2 1 holds 2 2 holds 8 3 holds 18 etc.
Orbital shapes are defined as the space that contains the electron 90% of the time. An orbital is a region within an energy level where there is a probability of finding an electron. This is a probability diagram for the… s orbital… in the first energy level.
Quantum Numbers: Electron Addresses! 1 st : Energy Level (n = 1, 2, 3, 4 …) Average distance of the electron in the electron cloud from the nucleus. 2 nd : Sublevel (l = s, p, d, f) Shape of electron cloud. energy levels have n sublevels. 3 rd : Orbital (m l ) Orientation of the cloud in 3-D space. s sublevels have 1 orbital (spherical) p sublevels have 3 orbitals(dumb bell shape) d sublevels have 5 orbitals(varied) f sublevels have 7 orbitals(varied) 4 th : Spin (m s = +1/2 or -1/2) Direction of electron spin. Each orbital holds 2 electrons, one with each spin.
Pauli Exclusion Principle: Each electron of an atom has its own unique set of quantum numbers. They may have three that are the same, but never all four.
Orbitals of the same shape (s, for instance) grow larger as n increases… Nodes are regions of low probability within an orbital. Sizes of s orbitals
The s orbital has a spherical shape centered around the origin of the three axes in space There is only one orientation for this shape
There are three dumbbell-shaped p orbitals in each energy level above n = 1, each assigned to its own axis (x, y and z) in space. P orbital shape
Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells ” …and a “dumbell with a donut”! d orbital shapes
In case you are too curious, here is what the f orbitals look like.
Energy Level (n) Sublevels in main energy level (n sublevels) Number of orbitals per sublevel Number of Electrons per sublevel Number of electrons per main energy level (2n 2 ) 1 2 3 4 Energy Levels, Sublevels, Electrons s 1 2 2 s 1 2 p 3 6 8 s 1 2 p 3 6 d 5 10 18 s 1 2 p 3 6 d 5 10 f 7 14 32
5g 18 6f 14 7d 10 8p 6 8s 2 The Diagonal Rule: Sublevels in order of increasing energy 1s 2 2s 2 3s 2 4s 2 5s 2 6s 2 7s 2 2p 6 3p 6 4p 6 5p 6 6p 6 7p 6 3d 10 4d 10 5d 10 6d 10 4f 14 5f 14 Aufbau Principle: Electrons fill the lowest energy position available. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 6 7s 2 5f 14 …
Energy levels and sublevels on the Periodic Table
Hund’s Rule: Electrons fill orbitals so that there are a maximum number of orbitals with a single electron.