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Lecture 15: The Hydrogen Atom

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Lecture 15: The Hydrogen Atom

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    1. Lecture 15: The Hydrogen Atom

    2. J.J. Thomson’s Plum Pudding Model of the Atom (1897)

    3. Rutherford’s a Scattering Experiment (1911)

    4. Discovery of the Atomic Nucleus

    5. Rutherford’s Solar System Model of the Atom

    6. Hydrogen Atom is Unstable? It is known that accelerating charges emit radiation Thus, electron should emit radiation, lose energy and eventually fall into the nucleus! Why doesn’t this happen? Shows that something was wrong with this model of the hydrogen atom

    7. Absorption Spectrum of a Gas

    8. Absorption spectrum of Sun

    9. Balmer’s Formula for Hydrogen Notice there are four bright lines in the hydrogen emission spectrum Balmer guessed the following formula for the wavelength of these four lines: where n = 3, 4, 5 and 6

    10. Bohr’s Model of the Hydrogen Atom (1913)

    11. Bohr’s Empirical Explanation Electrons can only take discrete energies (energy is related to radius of the orbit) Electrons can jump between different orbits due to the absorption or emission of photons Dark lines in the absorption spectra are due to photons being absorbed Bright lines in the emission spectra are due to photons being emitted

    12. Absorption / Emission of Photons and Conservation of Energy

    13. Energy Levels of Hydrogen

    14. Electron jumping to a higher energy level

    15. Spectrum of Hydrogen

    16. Hydrogen is therefore a fussy absorber / emitter of light

    17. This explains why some nebulae are red or pink in colour

    18. Schrödinger’s Improvement to Bohr’s Model Showed how to obtain Bohr’s formula using the Schrödinger equation Electron is described by a wave function y Solved for y in the electric potential due to the nucleus of the hydrogen atom

    19. Square Well Approximate electric (roller coaster) potential by a ‘square well’ System is then identical to the wave equation for a string that is fixed at both ends

    20. Vibrational Modes of a String

    21. Energy Levels in a Box

    22. Quantum Numbers Energy levels can only take discrete values Labelled by a ‘quantum number’ n, which takes values 1, 2, 3, ... Each level has energy that increases with n

    23. Ground State (n=1) Lowest or ground-state energy is non-zero Electron cannot sit still but must be forever ‘jiggling around’ Expected from the Heisenberg uncertainty principle

    24. Vibrational Modes of a Rectangular Membrane

    25. Electron in a Hydrogen Atom Wave function is like a vibrating string or membrane, but the vibration is in three dimensions Labelled by three quantum numbers: n = 1, 2, 3, … l = 0, 1, …, n-1 m = -l, -l+1, …, l-1, l For historical reasons, l = 0, 1, 2, 3 is also known as s, p, d, f

    26. 1s Orbital

    27. Density of the cloud gives probability of where the electron is located

    28. 2s and 2p Orbitals

    29. Another diagram of 2p orbitals

    30. 3d Orbitals

    31. 4f Orbitals

    32. Summary Electron does not fly round the nucleus like the Earth around the Sun (Rutherford, Bohr) Depending on which energy level it is in, the electron can take one of a number of stationary probability cloud configurations (Schrödinger)

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