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QUANTUM MECHANICS MAX PLANCK and the QUANTUM • electromagnetic energy could be emitted only in quantized form • E = hf, where E is energy, h is Planck's constant and f is the frequency of the radiation. Definition • Quantum: an indivisible entity. The magnitude can only take on certain discrete numerical values •The term “photon” was coined in 1926 by Gilbert Lewis •The QUANTUM of the electromagnetic field. Photons have zero mass and zero electric charge Photons do carry energy, momentum and angular momentum Photons are produced when one electron moves to an orbital of less energy And when an unstable nucleus undergoes nuclear decay And wherever charged particles are accelerated And atoms continuously emit photons due to their collisions with each other HYDROGEN LINE SPECTRUM Hydrogen Neon Nitrogen Argon Electromagnetic Spectrum THE WAVE-LIKE ELECTRON •Louis Victor de BroglieFrench Theoretical Physicist •1924 doctoral thesis, Recherches sur la théorie des quanta (Research on Quantum Theory), introduced his theory of electron waves. •Included the Wave-Particle Duality Theory of matter WAVE-PARTICLE DUALITY All objects exhibit, at times, a wave-like nature, and at other times a particle-like nature. •Photon acts like a PARTICLE •Photon acts like a WAVE •de Broglie suggested that there is a wave associated with the moving electron. The de Broglie Hypothesis Any moving particle or object has an associated wavelength •Not long after de Broglie showed that the electron could be connected with the wave, Heisenberg and Schrodinger described the waves mathematically. •Their formulas very closely match the experimental observations. Heisenberg Uncertainty Principle One cannot assign, with full precision, values for certain pairs of observable variables, including momentum and position, of a single particle at the same time. Schrödinger Wave Equation Schrödinger Wave Equation Leads to a series of mathematical functions called “wave functions”, Ψ. Ψ2 provides information about an electron’s location in an allowable energy state. Ψ2 = probability density THE QUANTUM MECHANICAL MODEL OF THE ATOM QUANTUM NUMBERS • Principal Quantum Number (n) refers to size and energy of orbital • Angular Quantum Number (l) Distinguishes the shape of the orbitals • Magnetic Quantum Number (ml) distinguishes orientation in space • Spin Quantum Number (ms) gives the 2 possible locations of the spin axis The s Orbital The p Orbital The d Orbitals The f Orbitals • much more complicated in their shape. • so much so that we are not going to worry about them in this course!!!!! •The maximum number of electrons that can occupy a certain energy level can be calculated from the equation 2n2 •Pauli Exclusion Principal: an atomic orbital may be described at most by two electrons •Aufbau Principal: electrons must enter orbitals of lowest energy first •Hund’s rule: when electrons occupy orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron with spins parallel. Then other electrons enter the orbitals with opposite spins. Arthur Compton The Compton Effect: When a high energy xray photon collides with a “free electron”, it gives some of its energy to the electron and a lower energy photon scatters off the electron. Momentum of a Photon the momentum of a photon is the quotient of Plank’s constant and the wavelength of the photon P = h/λ Page 857 References • http://hyperphysics.phyastr.gsu.edu/hbase/ems1.html • www.wikipedia.org • http://theory.uwinnipeg.ca/mod_tech/node154.html • http://library.thinkquest.org/19662/high/eng/electro n-wave.html • http://www.chemguide.co.uk/atoms/properties/atom orbs.html