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Recap – Last Lecture • 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. E = hν = hc/λ E = -2.18 x 10-18 J (1/n2final - 1/n2initial) Z2 • Theory and experiment agree closely…for hydrogen. 1 The Bohr model is too simple Most atomic spectra are much more complex than expected from a Bohr model of electron arrangements. (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 = h/mv • Heisenberg Uncertainty Principle – ‘fuzziness’ x v ≥ h/4m • Schrödinger Equation – energy of electron waves Ĥ = E 3 Wave – mechanical model • This can only be solved if various boundary conditions are applied. That is, the waves must be standing waves that are – continuous – single valued – multiples of a whole number of half wavelengths • There are then discrete solutions that represent the energy of each electron orbital. The orbitals are described by quantum numbers. 4 Quantum Numbers • The Principal Quantum Number : n n = 1, 2, 3 … Energy E=0 n=3 • Describes the size of the orbital n=2 • The larger the value of n, the bigger & the higher energy the orbital n =1 5 Quantum Numbers • The Angular Momentum Quantum Number : l l = 0, 1, 2 … (n -1) l=2 Energy l =1 n=3 l=0 l =1 n=2 l=0 n =1 l=0 6 Quantum Numbers 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 p orbital s orbital 7 Quantum Numbers • The Magnetic Quantum Number : ml ml = -l, -(l -1) … 0 … (l -1), l l=2 Energy 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 n=3 8 Quantum Numbers ml describes the orientation of the orbital if l = 0; ml = 0 if l = 1; ml = -1, 0, +1 (1 x s orbital) (3 x p orbitals) if l = 2; ml = -2, -1, 0, +1, +2 (5 x d orbitals) 9 Quantum Numbers • The Spin Quantum Number : ms ms = + 1/2 , — ½ • Describes the spin of the electron 10 Quantum Numbers • 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 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- n=2 l=0 ml = 0 2e- n =1 l=0 ml = 0 2e- 18e - 8e- 11 Shell Sub-shell Orbital Electrons Applications • 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 M e Fe Co Ni Cu Zn • Actual periodic table needs to be explained! 12 Learning Outcomes: • 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. − be able to complete the worksheet (if you haven’t already done so…) 13 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)? A. B. C. D. E. n=1 n=3 n=2 n=2 n=3 l=1 l=1 l=0 l=2 l=2 ml = 0 ml = +1 ml = -1 ml = +2 ml = 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? 14