VIEWS: 112 PAGES: 17 POSTED ON: 4/15/2011 Public Domain
SCH4U0 Tabone Uncertainty All measurements have a degree of uncertainty in them ocm 1cm 2cm 3cm We can tell that the blue bar is 2.3 cm for sure We can also estimate the next digit since the blue bar is clearly between the 3 and 4 mm mark, but this number is not 100% sure Therefore we say the blue bar is 2.35cm ± 0.02 The 0.02 is the uncertainty in the measurement Heisenberg Uncertainty Principle How do we observe anything? We often use light that bounces off an object to determine its position and speed We do the same with particles It turns out that the higher energy (lower wavelength) light we use, the more accurately we can determine the position of a particle But we have learned that light can impart momentum on particles... Heisenberg Uncertainty Principle Since light imparts momentum on particles, the act of observing them causes their behaviour to change The more accurately we try to determine their position (by increasing the energy of the light) the more momentum we give the particles. Meaning we know their momentum less accurately Heisenberg determined that there is always a certain degree of uncertainty in our knowledge of the behaviour of particles Heisenberg Uncertainty Principle The product of the uncertainties in position (x) and momentum (p) must always be larger than a constant ΔxΔp > h/4 This means that even if we only think of electrons as particles, we can never truly know everything about what they are doing in an atom We must then think in probabilities Schrödinger Wave Equation A physicist named Erwin Schrödinger developed an equation that describes the states of electrons in atoms and can be used to properly predict the emission spectra of atoms It is based on Louis de Broglie’s work with electron waves and utilizes the idea of probability in describing the actions of electrons Ψ (psi) is the symbol for the wave function It represents the set of probabilities (ψ) that the atom exists in different states Schrödinger Wave Equation The electrons are viewed as standing waves, and have only specific energies in each orbit due to their wavelength The atom can exist in many different states, with the electron in many different orbitals Schrödinger Wave Equation The atom is said to simultaneously exist in all of the possible states until one specific state “condenses” This idea is not very well understood, but it leads to interesting technology like touch screens The idea of states existing simultaneously is called “superposition” The superposition of states has famously been described using the “Schrödinger’s Cat” paradox Schrödinger’s Cat Hammer Fuzzy Cat Geiger Counter Poisonous Gas Radioactive Material Schrödinger’s Cat There is a 50% chance the radioactive material will decay in 1 hour and a 50% chance that it will not Meaning for that hour there is an equal chance that the cat is alive or dead – and we do not know which is true For that hour we say that the cat is both alive and the dead The state condenses into one or the other when we open the box and make an observation Electron Clouds Since we can’t know everything about the actions of electrons, we view orbitals as clouds of negative charge Each point in the orbital has a certain probability that the electron will be there at any given moment in time We picture orbitals as clouds of electron density Atomic Orbitals If the electron density of different orbital types (s, p, d, f) are graphed and modeled, we see that each type has its own characteristic shape We can also see the differences between the degenerate orbitals Degenerate orbitals often look similar but are arranged differently in space 3D Representations Atomic Orbitals Electron Density Atomic Orbitals Atomic Orbitals As n increases, the number of nodes in an orbital increases A node is a region where there is zero electron density Ex: 1s – 0 nodes, 2s – 1 node, 3s – 2 nodes etc. As l increases, the number of nodes decreases 3s – 2 nodes, 3p – 1 node, 3d – 0 nodes Quantum Tunnelling Using the probabilistic approach to viewing matter, every particle has a probability of existing anywhere But most of these probabilities are extremely small This can be used however to transport particles through and across barriers Ex: an alpha particle (helium nucleus) within a larger nucleus (like Ra) has a small probability of existing outside of the nucleus This is how radioactive decay occurs Ra-226 Rn-222 + He Quantum Tunnelling Quantum tunnelling is also the phenomenon behind touch screens The electrons in the screen have a small probability of being located in the sensors below the screen. As the screen is pushed and the screen moves closer the sensors beneath, the probability increases Eventually the probability is large enough that a significant (though small) number of electrons “jumps” from the screen to the sensors and starts an electric current