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History of Quantum Theory. Niels Bohr. Learning Goals. Students will be able to: u nderstand the Quantum Mechanical Model of the Atom understand how to describe the atom in terms of the Quantum Mechanical Model (energy level, shapes of orbits, sub-orbitals and quantum numbers).

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## History of Quantum Theory

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**History of Quantum Theory**Niels Bohr**Learning Goals**• Students will be able to: • understand the Quantum Mechanical Model of the Atom • understand how to describe the atom in terms of the Quantum Mechanical Model (energy level, shapes of orbits, sub-orbitals and quantum numbers)**Success Criteria**Students will: • record the important facts in an information chart. • understand the advancements of each new atomic model. • identify the weakness of the model that lead to further investigation.**Review – Rutherford’s Model**• Rutherford used the Gold Foil Experiment to theorize that: • atoms contain a tiny, dense, positively charged nucleus. • the nucleus was orbited by very light, negatively charged electrons. • most of the volume of an atom was empty space.**Limitations of Rutherford’s Model**• An electron accelerating around the nucleus would continuously emit electromagnetic radiation and lose energy • Therefore, it would eventually fall into the nucleus and the atom would collapse • However, this is not consistent with real-world observations – atoms are stable**Bohr and Quantum Theory**• Watch Structure of the Atom 4: The Bohr Model (9:08) http://www.youtube.com/watch?v=hpKhjKrBn9s • Bohr used recent work by Max Planck. • Planck and his teacher, Kirchhoff, studied the light emitted from hot, dark objects (blackbodies). • Planck noticed that when radiation (light, UV, IR) is emitted from a heated solid, the energy (blackbody radiation) is not released at all wavelengths, but is released at only specific wavelengths of energy • Energy is quantized. It comes in chunks.**Bohr and Spectroscopy**• A quanta is the amount of energy needed to move from one energy level to another. • Since the energy of an atom is never “in between” there must be a quantum leap in energy. • Bohr looked at the spectra released by light produced by an excited gas. • Bohr chose Hydrogen because it is the simplest element. • https://www.youtube.com/watch?v=LA9juHlyhKw (Mr. Causey – Bohr’s Planetary Model) • http://www.youtube.com/watch?v=Nv1_YB1IedE (Quantum Mechanics – The Fabric of the Cosmos – Brian Greene)**A short Review on Spectroscopy – remember grade 10!**(neither do I) • When white light is shone through a prism, it is broken into a spectrum. • Each colour corresponds to a different wavelength of light. • Each wavelength corresponds to a particular amount of energy.**Comparing Spectra**• Absorption spectra are produced when light is shone through a cooler gas. • Emission spectra are produced when light is emitted by the gas.**The Atomic Spectra of Hydrogen**• Bohr specifically used the spectra of hydrogen since it is the simplest of atoms.**Spectra of Other Atoms and Luminous Objects**• Note that each element has its own distinctive spectra.**Bohr-ing Math**• Bohr knew that he could measure the wavelength of the spectral lines. • When hydrogen is “excited” by the addition of energy (electricity is used in a gas discharge tube), an electron jumps up from a low orbit and moves into a higher orbit. • Eventually this electron falls back down and releases a specific amount of energy (a quanta). • When the electrons falls back down it emits energy that we can “see” as a spectral line. (note some lines appear in the infrared and ultraviolet portions of the spectrum)**Bohr-ing Math**• Bohr postulated that an electron cannot exist between orbits – electrons can only exist in orbits and each orbit occupies a specific energy level. • Each line in the spectrum is produced by the quantum of energy released when one electron falls back down to a lower orbit. • Examples: • drop from 4th orbital to 2nd orbital (blue line) • drop from the 3rd orbital to 1st orbital (ultraviolet line) • drop from 5th orbital to 3rd orbital (infrared line)**Wavelength Equation**• Bohr knew that the wavelength of light could be used to determine its energy level and its velocity using the equations below: • Bohr eventually expanded his math to determine the distance of each orbital from the nucleus and the energy level of each permissible energy level for hydrogen.**Successes and Weaknesses of Bohr’s Model**• Successes • Bohr’s mathematics explained all the observations for Hydrogen perfectly • This is a major success for Quantum Mechanics – to this day it has never failed • He solved Rutherford’s problem • Weaknesses • Bohr’s method only worked for Hydrogen • Although the quantum theory of light was experimentally proven, other experiments had proven that light had also continuous wavelike properties. Einstein suggested that there were "two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do". Hence light and photons display wave and particle properties**deBroglie(1924) & Schrödinger (1925)**• Responding to the difficulties in the Bohr model, Louis deBroglie , from France, suggested that matter like light, has the properties of both particles and waves. This particle-wave duality -derived from the work of Einstein and Planck - was experimentally confirmed, for the electron, in 1927. • Austrian physicist Erwin Schrodinger formed a model of a complete atom as interacting waves. • The particles became like vibrations on a violin string, only they were closed in circles. • His partial differential equation seemed to bear a similar relation to the mechanics of the atom as Newton's equations of motion bear to planetary astronomy.**deBroglie(1924) & Schrödinger (1925)**• A representation of energy levels and sub-levels as waves instead of particles in circular orbits. Note the math – Schrodinger’s wave function being applied.**Heisenberg (1926)**• German physicist Werner Heisenberg formulated his Uncertainty Principle which says that you cannot know by measurement the position and momentum of a particle simultaneously. • The better you know one, the worse you know the other. • Particles and fields undulate and jump between all possible values consistent with the quantum uncertainty. • Atoms were now visualized as a nucleus surrounded by a cloud of electrons distributed according to a wave pattern by the Schrodinger equation. Clouds of electrons determined by Heisenberg and Schrodinger’s mathematical models and borne out by X-ray studies.**Dirac (1926)**• Paul Dirac devised a form of quantum mechanics (developed by Schrodinger and Heisenberg), which provides the laws of motionthat govern atomic particles. • The electron could now be described by four wave functions, satisfying four simultaneous differential equations. As before the electrons still cannot be pinpointed but exist as a sort of cloud of probability outside the nucleus. • It followed from Dirac's equations that the electron must rotate, or spin, on its axis, and also that there must be states of negative energy.**Quantum Numbers**• Using high resolution spectra, Michelson noticed that the main lines found in spectra were often split into smaller lines. • Sommerfeld (1915) was able to explain these small lines using elliptical orbits. • deBroglie and schrodinger’s work clarifies this • He explained that each level has sub-levels or subshells. • Therefore each one of Bohr’s energy levels can be divided into smaller levels.**Secondary Quantum Number**• BOHR – his energy levels (orbitals) were labeled the Primary Quantum Number (n) • SOMMERFELD – Secondary Quantum Number (l) • l = 0 to n-1, • therefore if l = 3, n can equal 0, 1, 2 • Therefore the 3rd energy level contains 3 sublevels. • The secondary quantum number caused orbitals to take on different shapes • l = 0 (speherical orbital) • l = 1 (dumb-bell shaped 2-lobed orbitals) • l = 2 (4-lobed orbitals) • l = 3 (6 and 8-lobed orbitals)**Magnetic Quantum Number**• Zeeman (1896) noticed that the spectral lines could also be split if placed in a magnetic field. • Sommerfeld and DeBye used this information to produce another Quantum number, the Magnetic Quantum Number (ml) • ml = -l to +l • Therefore if l = 1; ml can be -1, 0, +1 • This means that each sublevel can have further sublevels. • This causes the orbitals to have different orientations in space**Spin Quantum Number**• Work by Pauli (1925) determine that two electrons could occupy each orbital. • These electrons have opposite spins given the values +1/2 and -1/2. • The Spin Quantum Number (ms) • ms = -l/2 and +l/2 • This means that each sublevel can be occupied by two electrons!**Summary**• This time line draws nice comparisons between the Quantum view of the Atom with the Bohr-Rutherford model and the Lewis Structures we have used in the past.**Senior Physics – TVO programs**• Structure of the Atom 1: The Earliest Models (9:04) http://www.youtube.com/watch?v=BhWgv0STLZs • Structure of the Atom 2: Smaller than the Smallest (8:47) http://www.youtube.com/watch?v=WmmglVNl9OQ • Structure of the Atom 3: The Rutherford Model (9:10) http://www.youtube.com/watch?v=FfY4R5mkMY8 • Structure of the Atom 4: The Bohr Model (9:08) http://www.youtube.com/watch?v=hpKhjKrBn9s • Structure of the Atom 5: Spectra (9:28) http://www.youtube.com/watch?v=5z2ZfYVzefs • Structure of the Atom 6: The Wave Mechanical Model (9:08) http://www.youtube.com/watch?v=IsA_oIXdF_8 • These programs provide excellent review of the History of the Atomic Model and how Quantum Mechanics is important!

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