* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Recap – Last Lecture The Bohr model is too simple Wave
Probability amplitude wikipedia , lookup
Density matrix wikipedia , lookup
Path integral formulation wikipedia , lookup
Renormalization group wikipedia , lookup
Spin (physics) wikipedia , lookup
Renormalization wikipedia , lookup
Quantum field theory wikipedia , lookup
Quantum entanglement wikipedia , lookup
Coherent states wikipedia , lookup
Quantum dot wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Quantum fiction wikipedia , lookup
Double-slit experiment wikipedia , lookup
Bell's theorem wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Quantum computing wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Matter wave wikipedia , lookup
Quantum teleportation wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Particle in a box wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Quantum key distribution wikipedia , lookup
Quantum machine learning wikipedia , lookup
Tight binding wikipedia , lookup
Atomic theory wikipedia , lookup
Canonical quantization wikipedia , lookup
Wave–particle duality wikipedia , lookup
Quantum group wikipedia , lookup
History of quantum field theory wikipedia , lookup
EPR paradox wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Quantum state wikipedia , lookup
Molecular orbital wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Hidden variable theory wikipedia , lookup
Hydrogen atom wikipedia , lookup
Recap – Last Lecture The Bohr model is too simple • Bohr model of the atom: electrons occupy orbits of certain energies. • Evidence of this from atomic spectra in which wavelength of light is related to energy difference between orbits. Most atomic spectra are much more complex than expected from a Bohr model of electron arrangements. E = hν = hc/λ ΔE = -2.18 x 10-18 J (1/n2final - 1/n2initial) Z2 • Theory and experiment agree closely…for hydrogen. 1 Wave – mechanical model (http://chemistry.bd.psu.edu/jircitano/periodic4.html) 2 Wave – mechanical model • Light has a dual nature and the de Broglie equation relates wavelength to momentum • This can only be solved if various boundary conditions are applied. That is, the waves must be standing waves that are λ = h/mv – continuous – single valued – multiples of a whole number of half wavelengths • Heisenberg Uncertainty Principle – ‘fuzziness’ Δx Δv ≥ h/4πm • Schrödinger Equation – energy of electron waves Ĥψ = Eψ 3 • There are then discrete solutions that represent the energy of each electron orbital. The orbitals are described by quantum numbers. 4 1 Quantum Numbers Quantum Numbers • The Principal Quantum Number : n n = 1, 2, 3 … • The Angular Momentum Quantum Number : l Energy l = 0, 1, 2 … (n -1) E=0 l=2 Energy l =1 n=3 • Describes the size of the orbital n=3 l=0 n=2 • The larger the value of n, the bigger & the higher energy the orbital l =1 n=2 l=0 n =1 l=0 n =1 5 Quantum Numbers Quantum Numbers • The Magnetic Quantum Number : ml ml = -l, -(l -1) … 0 … (l -1), l l describes the shape of the orbital d orbital Quantum no Orbital description l=0 s orbital l=1 p orbital l=2 d orbital l=3 f orbital 6 l=2 Energy p orbital n=3 s orbital 7 ml = -2,-1,0,+1,+2 l =1 ml = -1,0,+1 l=0 ml = 0 l =1 ml = -1,0,+1 n=2 l=0 ml = 0 n =1 l=0 ml = 0 8 2 Quantum Numbers Quantum Numbers ml describes the orientation of the orbital if l = 0; ml = 0 if l = 1; ml = -1, 0, +1 • The Spin Quantum Number : ms ms = + 1/2 , — ½ (1 x s orbital) (3 x p orbitals) • Describes the spin of the electron if l = 2; ml = -2, -1, 0, +1, +2 (5 x d orbitals) 9 Quantum Numbers Applications • Each orbital, uniquely described by n, l and ml, may contain a maximum of two electrons, one spin + 1/2, the other spin -1/2 . l=2 Energy n=3 n=2 n =1 Shell ml = -2,-1,0,+1,+2 10e - l =1 ml = -1,0,+1 6e- l=0 ml = 0 2e- l =1 ml = -1,0,+1 6e- l=0 ml = 0 2e- l=0 ml = 0 Sub-shell 10 Orbital 18e - • Bohr model results in a periodic table with a 2, 8, 18 pattern H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ne Sc Ti V Cr Me Fe Co Ni Cu Zn • Actual periodic table needs to be explained! 8e- 2eElectrons 11 12 3 Learning Outcomes: • Questions to complete for next lecture: 1. Provide a valid set of quantum numbers, n, l and ml, of an electron in a 4p orbital? (Question form 2015 exam) 2. Which of the following is a valid set(s) of quantum numbers and identify the incorrect number in the other set(s)? By the end of this lecture, you should be able to: − Explain the meaning of the orbital quantum numbers, n l ml ms. − Understand the designation of orbitals such as 1s, 3d, 4p, 4f. − Recognise the shapes of s, p and d atomic orbitals. − Determine the number of electrons in an orbital/ sub-shell/shell. A. B. C. D. E. n n n n n =1 l=1 = = = = 3 2 2 3 l l l l = = = = 1 0 2 2 ml ml ml ml ml =0 = = = = +1 -1 +2 0 ms ms ms ms ms = +1/2 = = = = +1/2 -1/2 -1/2 0 3. Sketch the shape of a px orbital. How many electrons can it accommodate? 4. Which quantum number describes the shape of an orbital? 5. How many sub-shells are there in the n = 3 shell? − be able to complete the worksheet (if you haven’t already done so…) 13 14 4