# If we plot height of the water surface vs the

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If we plot height of the water surface vs. the distance from the center on the horizontal axis, we get a mathematical function that looks similar to an electron wavefunction. Compare

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4 Waves and Electrons We describe the behavior of electrons with wavefunctions. The wavefunction squared represents the probability of finding an electron in space. [three functions are plotted below vs. distance from the nucleus] The 3s orbital (r = distance from nucleus) Red = wavefunction Ψ Blue = Ψ 2 to give the probability of finding electron in a certain volume Green = Ψ 2 multiplied by volume to see the most probable location for an electron (volume corrected plot) [scales are different for each function] Wavefunctions The wavefunction (a 3D function) has a certain value in each point of space. The square of this function represents probability of finding an electron in a minuscule amount of space around that point. Orbitals, as represented by wavefunctions squared, are places (volumes of space) where probabilities of finding an electron are non-zero, i.e. places where the electrons are allowed to be. The probability of finding an electron in a volume of space is called electron density; it is a fraction of an electron per unit volume. The pictures we draw of orbitals represent 90-95% probabilities; these are time independent.
5 Review of Quantum Numbers Principal quantum number (shell) n =1, 2, 3 Angular momentum quantum number l ; depends on n .

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