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Dr. Jie ZouPHY 13711 Chapter 42 Atomic Physics (cont.)
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Dr. Jie ZouPHY 13712 Outline The quantum model of the hydrogen atom The wave functions for hydrogen
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Dr. Jie ZouPHY 13713 The quantum model of the hydrogen atom Difficulties with Bohr theory: Many of the lines in the Balmer and other series of hydrogen are not single lines at all. Splitting of spectral lines when atoms are placed in a strong magnetic filed. Need a full quantum model involving the Schrödinger equation to describe the hydrogen atom.
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Dr. Jie ZouPHY 13714 The quantum model of the hydrogen atom General strategy: Solving the Schrödinger equation for the hydrogen atom The three-dimensional time-independent Schrödinger equation: Formal procedure for solving the problem: The potential energy function for the hydrogen atom: Substitute U(r) into the Schrödinger equation and find the appropriate solutions to the equation satisfied by appropriate boundary conditions.
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Dr. Jie ZouPHY 13715 Results for a Hydrogen atom Three different quantum numbers for each allowed state of the hydrogen atom ( ): Principal quantum number, n: The energies of the allowed states for the hydrogen atom depend only on n, Orbital quantum number, l Orbital magnetic quantum number, m l
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Dr. Jie ZouPHY 13716 Relationship among the three quantum numbers
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Dr. Jie ZouPHY 13717 Atomic shell and subshell notations
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Dr. Jie ZouPHY 13718 Example: The n=2 level of Hydrogen For a hydrogen atom, determine the number of allowed states corresponding to the principal quantum number n = 2, and calculate the energies of these states.
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Dr. Jie ZouPHY 13719 The wave functions for Hydrogen Wave function in the ground state 1s: Radial probability density function P(r) = 4 r 2 | | 2. For the hydrogen atom in its ground state:
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Dr. Jie ZouPHY 137110 Hydrogen atom in its ground state The charge of the electron is extended throughout a diffuse region of space - Electron cloud
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Dr. Jie ZouPHY 137111 Example: Probabilities for the electron in hydrogen Calculate the probability that the electron in the ground state of hydrogen will be found outside the first Bohr radius, a 0.
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Dr. Jie ZouPHY 137112 Example: The ground state of hydrogen Calculate the most probable value of r for an electron in the ground state of the hydrogen atom.
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Dr. Jie ZouPHY 137113 Homework Chapter 42, P. 1393, Problems: #19, 20.
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