* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download CHE 106 Chapter 6
Relativistic quantum mechanics wikipedia , lookup
Photosynthesis wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
Ferromagnetism wikipedia , lookup
Particle in a box wikipedia , lookup
Bremsstrahlung wikipedia , lookup
Chemical bond wikipedia , lookup
Double-slit experiment wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Molecular orbital wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Auger electron spectroscopy wikipedia , lookup
Matter wave wikipedia , lookup
Tight binding wikipedia , lookup
Hydrogen atom wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Wave–particle duality wikipedia , lookup
Electron-beam lithography wikipedia , lookup
Atomic theory wikipedia , lookup
CHE 106 Chapter 6 The Dual Nature of Light Much of what we know about electronic structure – the arrangement and energies of electrons around the nucleus came from studying the light that atoms both absorb and release. Dual Nature of Light: Light behaves both as a wave and particle (photons). Even electrons and other solid particles can exhibit wavelike properties. Much of our experience with light has been light as visible light, but visible light is only one type of electromagnetic radiation. There are many other types of ER or radiant energy – x-rays, infrared, gamma etc. They transmit energy in a wavelike behavior, much as waves in the ocean. The Dual Nature of Light Properties of waves: Wavelength: distance between two adjacent peaks or troughs Frequency: the number of complete wavelengths that pass a given point in one second These two variables can be related to the speed of light which is defined as: c = lu l: wavelength (lambda) u: frequency (nu) cycles/sec = Hertz (Hz), s-1 or /s C: speed of light: 3.0 x 108 m/s The Dual Nature of Light Example: A laser is used in eye surgery to fuse detached retinas and produces radiation with a frequency of 4.69 x 10-14 s-1. What is the wavelength of this radiation? The Dual Nature of Light Although much of our experience with light is as a wave, the wave-like properties of light could not be used to explain several other phenomena: blackbody radiation, the photoelectric effect and emission spectra of elements. The Dual Nature of Light • Light has both wave-like and particle-like nature Particulate Behavior Wave-like Behavior electrons ejected from bulk material Photoelectric Effect White Light Source Dispersion by Prism The Dual Nature of Light • Matter has both wave-like and particle-like nature Particulate Behavior Wave-like Behavior electrons ejected Electron Ionization Electron Beam Source Electron Diffraction The Dual Nature of Light Blackbody Radiation: Max Planck When objects are heated, the give off radiation. And this radiation is related to the temperature. Red Hot vs. White Hot: Different color and intensity of radiation is dependent on temperature. Classical physics could not explain the relationship between temperature and the color of the emitted light. The Dual Nature of Light Max Planck was able to explain this phenomena by assuming that energy can be released in discrete packets called quanta. Quanta: the minimum energy absorbed or emitted, whose energy is related to it’s frequency. E = hv Where h is Planck’s constant = 6.626 x 10-34 J-s. The Dual Nature of Light How to interpret Planck’s equation: “As the frequency of radiation increases, the energy of that radiation increases by the increment “h”.” source:http://www.kentchemistry.com/links/AtomicStructure/PlanckQuantized.htm So only certain energies are “allowed”, all energy must be a multiple of Planck’s constant. So in that regard – energy is quantized – it only exists in distinct quantities. It is not continuous. The Dual Nature of Light The Dual Nature of Light Light energy may behave as waves or as small particles (photons). Particles may also behave as waves or as small particles. Both matter and energy (light) occur only in discrete units (quantized). Quantized (can stand only on steps) Non-Quantized (can stand at any position on the ramp) The Dual Nature of Light A laser emits light with a frequency of 4.69 x 1014 s-1. What is the energy of one quantum of this energy? ANSWER: 3.11 X 10-19 J The laser emits in energy in pulses of short duration. If the laser emits 1.3 x 10-2 J of energy during a pulse. How many quanta of energy are emitted during the pulse? ANSWER: 4.2 x 1016 quanta The Dual Nature of Light Albert Einstein and the Photoelectric Effect When light with a certain amount of energy is shone on a surface, it can cause the surface to emit electrons. Different materials require different frequencies of light in order to observe this effect. Einstein built upon the idea of light as a particle to explain this phenomena. He used Planck’s equation to assume Energy of photon = hv The Dual Nature of Light Photoelectric Effect: Discrete particles of light called photons strike the surface and transfer all of their energy to the electrons on the surface of the metal. With enough energy, electrons can overcome the attractive forces holding them to the surface and bounce off the metal. This can generate a measurable voltage and generate electricity. The Dual Nature of Light The Dual Nature of Light De Broglie – particles (photons, electrons, matter) will behave like particles and like waves, depending on the circumstance and what we are trying to observe: l = h/mv M = mass; v = velocity; h = Planck’s constant. Examples: A 0.1 kg fastball traveling at 20 meters/sec will have a wavelength of 3 x 10-22 pm. A 9 x 10-31 kg electron travelling at 1 x 105 m/s will have a wavelength of 7000 pm. The Dual Nature of Light Neils Bohr: Explanation of Emission Spectra A source of radiation often emits radiation that can be broken down into a continuous spectra – just like visible light through a prism will form a continuous rainbow. However, certain elements would not produce a continuous spectrum. Only light of certain wavelengths would be present = line spectrum. The Dual Nature of Light The first spectra to be studied was that of hydrogen. With only 1 electron – the spectrum was relatively simple: 4 lines. Johann Balmer was able to write an equation that would allow us to calculate the wavelengths of all the spectral lines of hydrogen. Rh = 1.09776 x 107 m-1 Where n2 is greater than n1 The Dual Nature of Light Bohr used this to explain hydrogen’s emission spectra: relating the different wavelengths being produced to the energy transitions between principle energy levels. He proposed the electrons travel in circular orbits around the nucleus, and each orbit has a quantized energy state. When electrons change state, the energy that is either gained or emitted is equal to the energy difference between states. The Dual Nature of Light With this he was able to manipulate Rydberg’s equation to calculate the energy for electrons in each orbit: En = (-RH)(1/n2) And the energy associated with transitions: DE = (-RH) 1 _ 1 2 2 in fn Rydberg’s constant is redefined in this equation as -Rhhc so Rh = 2.18 x 10-18 J and n = principal quantum number The Dual Nature of Light Sample exercise: Calculate the wavelength of hydrogen emission line that corresponds to the transition of the electron from the n=3 to the n=1 state. 1. Solve for energy: 1. 1.94 x 10-18 J 2. Solve for frequency: 1. 2.92 x 1015 s-1 3. Solve for wavelength: 1. 1.03 x 10-7 m In what portion of the electromagnetic spectrum is this line found? 103 nm = ultraviolet Wave Behavior of Matter Finally, Louis de Broglie further extended the idea of energy behaving as a particle and wave. Any particle – energy or matter can behave then as a wave (our interests are electrons). The wavelength is dependent upon it’s mass and velocity: l= h mv The wavelength for most objects is so small, it is not observable because there mass is so large. However, for electrons – which have a incredibly small mass, their wavelengths become more important. Wave Behavior of Matter Example: At what velocity must a neutron be moving in order for it to exhibit a wavelength of 500 pm? ANSWER: 7.94 X 102 m/s Wave Behavior of Matter X-ray diffraction: when x-rays which are considered to exhibit wavelike properties are passed through a crystal, the waves are diffracted in a specific pattern. http://www.pbs.org/wgbh/nova/photo51/ The Dual Nature of Light Wave Behavior of Matter When similar work was done with electrons moving at a high velocity, they also produced a diffraction pattern as the waves interacted with the structure of the sample. Electrons moving as a wave and bouncing off structures as small as atoms is the basis for the electron microscope. The electron microscope can magnify things nearly three million times because the wavelength of electrons is so much smaller than that of visible light. The Uncertainty Principle When electrons can be thought of to have wavelike properties, this makes it much more difficult to describe an exact location. Waves extend in space and their location cannot be specifically defined to one particular point at a given time. So then, how can we estimate the location of the electrons in an atom? Can we determine where an electron is located at a particular moment in time in an atom? Uncertainty Principle Werner Heisenberg: Proposed that there is a limitation on how much of the location and the momentum of an object at given time. The uncertainty principle states: it is impossible for us to know simultaneously both the exact momentum of the electron and its exact location in space. The act of measuring affects what we are measuring: (Dx)D(mv) > h / 4P Quantum Mechanics and Atomic Orbitals. Erwin Shrodinger: Shrodingers equation Leads to wave functions that describe the location of electrons in an atom. Wave funtions are symbolized with the letter y (Greek: psi). When y is squared (Y2) – it gives us the probability distribution of an electron in atom. Rather than knowing an exact location, Shrodinger’s equations gives us regions of probability where an electron is found. Quantum Mechanics and Atomic Orbitals. The intersection of the three axises represent the nucleus. This electron density distribution shows that where the more intense color, the greater the value of Y2… there is a greater chance of finding an electron. These regions are a certain amount of energy and will also have specific shapes depending on the type of orbital. Quantum Mechanics and Atomic Orbitals. The wave functions gave rise to the orbitals, each with a shape and energy. This was a much different model than Bohr had proposed for hydrogen. Bohr proposed principal quantum number: “n” which corresponded with the orbits. The quantum mechanical model uses n, l, m1. Quantum Mechanics and Atomic Orbitals. Principal Quantum Numbers (n): can have integral values > 0 ( 1, 2, 3 ,4 etc.) . - As n increases, the electron density is farther away from the nucleus. Size of orbital increases. - As n increases, the electron is less tightly bound and has more energy Angular Momentum Azimuthal Quantum Number (l): Can have integral values from 0 to n-1. Defines the 3D shape of the orbital. Rather than lists as numbers, often referred to by letter: S=0 p=1 d=2 f=3 Quantum Mechanics and Atomic Orbitals. Magnetic Quantum Number ‘ml’: has integral values between ‘l’ and ‘–l’. Describes how the orbital is arranged in space. - A collection of orbitals with the same value of ‘n’ is the electron shell - A collection of orbitals with the same value of n and l belong to the same subshell. Quantum Mechanics and Atomic Orbitals. Example: Electron orbitals with a principle number of 3 would have the following available values n: principal quantum number 3 l: Subshell Ml azimutha designati l on Number of orbital in each 0 1 2 1 3 5 3s 3p 3d 0 -1,0,1 -2,1,0,1,2 Quantum Mechanics and Atomic Orbitals. A couple of patterns that exist: Each shell is divided into a number of subshells, equal to the principal quantum number. Each subshell is divided into orbitals, that increase by odd numbers. Quantum Mechanics and Atomic Orbitals Combinations of the quantum numbers specifies which specific electron we are referring to in an atom (address) n l subshell 1 2 0 0 1 0 1 2 3 1s 2s 2p 3s 3p 3d ml no. of orbs no. of e-l 0 1 2 2 0 1 2 8 1, 0, -1 3 6 0 1 2 1, 0, -1 3 6 18 2, 1, 0, -1, -2 5 10 Quantum Mechanics and Atomic Orbitals Quantum Numbers also specify energy of the occupying electrons, l=0 l=1 l=2 l=3 n=• 0 n=4 n=3 E N E R G Y n=2 4s 3s 4p 3p 2s 2p 4d 3d 2+6=8 electrons 2 electrons max max n=1 1s 4f 2+6+10+14= 32 electrons max 2+6+10=18 electrons max Quantum Mechanics and Atomic Orbitals. Example: What is the designation for the subshell with n = 5 and l = 1? How many orbitals in this subshell? Indicate the value of ml for each. N = 5 is 5th principal energy level L = 1 is the p sublevel P has 3 orbitals 3 orbitals are labeled -1, 0, 1 Orbitals Ground State: electron is in the the lowest energy orbital available. Excited State: electron is in another orbital – presumably by gaining energy. All orbitals of the same l value are the same shape. Depending on the n value – they will differ in size and relative energies. Orbitals Orbitals The 1s orbital is a symmetrical spherical. A plot of the distribution Y2 versus the distance (r) from the nucleus shows that as the radius gets farther, the probability of finding an electron drops off significantly. Orbitals The higher energy s orbitals are also spherical and symmetrical. However, there are regions of zero electron density, called nodes. 2s has 1 node, 3s has 2 nodes. - In the higher s orbitals, the electron density distribution tells us that there is a higher probability of finding an electron farther away from the nucleus. Orbitals In the p orbitals, the electron density is concentrated in two regions (two lobes) on either side of the nucleus… considered “dumbbell” shaped, with a node at the nucleus. In the p sublevel – there are 3 orbitals ( 3 dumbbells), and they differ in their orientations around the nucleus (origin). Orbitals l=1 p Orbitals y y z py px x y z x x 2p y 2 (p) z z pz Radial Electron Distribution 3p x radius Orbitals Orbitals In the third shell and beyond, we see the d sublevels – with five d orbitals. Orbitals In the 4th shell and beyond, we encounter the f orbitals which are very complicated to represent. The shapes of the orbitals and how many are in each sublevel will assist you in understanding how molecules bond and exchange/share electrons. Orbitals Orbitals All of this is based on the hydrogen atom, because the mathematical equations are relatively simplistic when dealing with only one electron. While the shapes o the orbitals are essentially the same from Hydrogen to multi-electron atoms, the energies differ drastically. For hydrogen, the energy is largely dependent on the value of n. For bigger atoms the sublevel (l) also plays a role because now we have to worry about electron – electron repulsion. Many Electron Atoms In the graph below, the 2s orbital has less energy than the 2p orbital… and this can be attributed to like charge repulsion as well as the effective nuclear charge on electrons. Many Electron Atoms In atoms with more than one electron, there are two forces acting on each electron at the same time: 1. Attraction to the protons in the nuclear 2. Repulsion by other electrons To understand the energy of the electron, we have to know the net “feeling” each electron experiences in it’s environment. Many Electron Atoms The net attractive force that an electron will feel is called the effective nuclear charge: Zeff Zeff = Z – S Where Z = nuclear charge and S = screening value. The screening value is the average number of other electrons between the electron in question and the nucleus. ** The effective nuclear charge is always less than the full nuclear charge** Many Electron Atoms Zeff = Z - S Average electronic charge (S) between the nucleus and the electron of interest The larger the Zeff an electron feels leads to a lower energy for the electron r Z Electrons outside of sphere of radius r have very little effect on the effective nuclear charge experienced by the electron at radius r Many Electron Atoms For a given n value, the Zeff decreases with increasing values of l. The effective nuclear charge will depend on what type of sublevel and therefore number of orbitals are participating in the screening. Screening ability: s>p>d>f Many Electron Atoms Example: The sodium atom has 11 electrons. Two occupy a 1s orbital, two occupy a 2s orbital and one occupies a 3s orbital. Which of these s electrons experience the smallest effective nuclear charge? Answer: 3s electrons because they have a greater number of electrons between them and the nucleus (S increases). So Zeff decreases and energy increases. Many Electron Atoms With a principal quantum number, 3s electrons will experience less screening/shielding than the 3d electrons. So the 3d electrons have less Zeff. In a many electron atom, for a given ‘n’.. Zeff decreases as ‘l’ increases. Because Zeff decreases for 3d electrons, they will have more energy. In a many electron atom, for a given ‘n’… the energy level of an orbital increases as ‘l’ increases. Electron Spin Electrons have spin properties – in which they spin along an axis. Electron spin: ms. The spinning electrons produces two magnetic field: in opposite directions Electron spin is quantized: ms = +1/2 or -1/2 Because two electrons can be in the same principal energy level, sublevel and orbital – they will share 3 of the 4 principal quantum numbers: n, l, ml. They must have a different 4th principal quantum number: ms. Electron Spin N - Magnetic Fields - N Electron Spin Pauli Exclusion Principle: No two electrons can have the same set of four quantum numbers n,l, ml and ms. In order to put electrons in the same orbital, they must have different ms numbers = opposite spins. Electron Configurations Electrons fill in order of increasing energy, with no more than two electrons per orbital. Reminder: two electrons will not occupy the same orbital before each orbital has at least one. Why? Degenerate orbitals are orbitals that are all at the same energy level. Hund’s Rule: the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons with the same spin. Electron Configurations Guidelines for electron configurations: - Obey Pauli Exclusion Principle - Obey Hund’s Rule - Fill from lowest to highest energies - Shorthand: - Na: 11 electrons: 1s22s22p63s1 or [Ne]3s1 - Closed shell (filled), half filled and empty orbital configurations most stable - Outer electrons are valence electrons - Inner electrons are core electrons. Electron Configurations After argon with 18 electrons, potassium was studied and its outermost electron was found in an s orbital, rather than the 3d sublevel. Which mean the the 4s sublevel must have less energy than the 3d. After calcium the 4s is filled, and the the next 10 elements begin filling the d sublevel. After 3d is filled then 4p is filled for the remaining elements in that row. This pattern repeats itself for the remaining rows in the periodic table, with n increasing by 1 as you go down. Electron Configurations Electron Configurations The transition metals are also referred to as the “d block” while the Lanthanide and Actinide series at the bottom of the periodic table is known as the “f block”. Many of them are radioactive and rarely found in nature. By knowing the location of an element on the periodic table, elements fall into categories depending on their electron configurations. Electron Configurations S Block: First two groups on the periodic table P Block: Six rightmost groups on the PT Together – these makeup our main group elements. D Block: 10 elements (transition elements) F Block: Lanthanide and Actinide Series **The number of columns in each block is equal to the number of electrons required to fill that sublevel.** Electron Configurations To write the electron configuration for Selenium: To use shorthand, we are able to start with the noble gas core which in this case is argon. Se: [Ar] Then you are able to work your way across the periodic table until you get to selenium: 4s23d104p4. Final: [Ar]4s23d104p4. Electron Configurations Example: What family of elements is characterized by having an ns2p2 outer electron configuration? ANSWER: Group 14 or Group IVA Example: Use the periodic table to write the e- configurations for the following atoms by giving the appropriate noble gas inner core plus the electrons beyond it: Co, Te. Co: [Ar]4s23d7 Te: [Kr]5s24d105p4