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Lecture 6

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Thottackad Radhakrishnan

Lecture 6 Friday, 17 January, 2014 11:03 AM Today's Topics: Announcements: Homework: •  DV2035 - go to office hours Lecture Topic: Wave Equation Derivation- know it H, the Hamiltonian can be given as • • Where is called the wave function ○ It is a function of the coordinates x, y, z of the electron's position in three dimensional space • H represents a set of mathematicalinstructions called an operator ○ In this case H, the Hamiltonian operatoracts on function to give back multiplied by a constant called E which represents the total energy of the atom PE + KE ○ If • Transformationfrom Cartesian coordinatesto polar coordinates Orbitals in the wave equation: • ○ Where • An orbital is just a three-dimensional plot of a mathematicalequation: ○ Schroëdinger Equation: 2 2 • Interpretation of Ψ, Ψ , and ∫Ψ dV ○ Ψ - wave function/equation, atomic orbital ○ Ψ - a measure of the intensity of electrondensity distribution 2 ○ ∫Ψ - probability of finding the electron within a certain volumeelement, dV • Boundary conditions on Ψ ○ Must be finite ○ Must be single valued ○ Must be continuous ○ (normalization) ○ Total probability of finding the electron is 1 Principle Quantum Number, n • Recall: Ψ givs probability of finding an electron in a given location • 90% of the electron density is found in the 1s orbital ○ Center of the orbital will have higher probability because it is a smaller volumewith many electrons due to the attractionbetween the electrons and the protons in the nucleus • "n" determines the size of this 90% boundary • Bohr theory says electron is found in the first orbit (and only in that specific orbit) • B
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