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QUANTUM THEORY AND ATOMIC STRUCTURE The Nature of Light Visible light is one type of electromagnetic (EM) radiation, also called electromagnetic energy and radiant energy. Other types include x-rays, microwaves and radio waves All EM radiation consists of energy propagated by means of electric and magnetic fields that alternately increase and decrease in intensity as they move through space This classical wave model distinguishes clearly between waves and particles. The Wave Nature of Light c=νxλ Frequency (ν, greek nu) is the number of cycles the wave undergoes per second, and is expressed in units of 1/second (s-1 also called hertz, Hz) Wavelength (λ, greek lambda) is the distance between any point on a wave and the corresponding point on the next wave; the distance the wave travels during one cycle. It expressed in meters and often in nanometers (nm, 10-9 m) picometers (pm, 10-12 m)or angstorm (, 10-10 m) Amplitude (intensity) of a wave is represented by the height of the crest (or depth of the trough) of the wave The Electromagnetic Spectrum The waves in the spectrum all travel at the same speed through a vacuum but differ in frequency and therefore, wavelength Sample Problem A dental hygienist uses x-rays (λ = 1.00 ) to take a series of dental radiographs while the patient listens to a radio station (λ = 325 cm) and looks out the window at the blue sky (λ = 473 nm). What is the frequency (in s-1) of the electromagnetic radiation from each source? Assume that the radiation travels at the speed of light 3.00 x 108 m/s) Solution Converting from angstroms to meters = 1,00 Ǻ x 10-10 m/1 Ǻ = 1,00 x 10-10 m = c/ = 3,00 x 1018 s-1 Radio station : = c/ = 9,23 x 107 s-1 Blue sky = = c/ = 6,34 x 1014 s-1 The Distinction between Energy and Matter Interference •constructive interference: amplitudes add peaks, troughs of interfering waves occur in the same positions (waves are in phase ) •destructive interference: amplitudes cancel peaks of one wave are in same position as troughs of the other (waves are out of phase ) Diffraction Three ways to tell a wave from a particle a wave can't bend around obstacles much larger than its wavelength what does this imply about the wavelength of sound waves? radio waves? visible light? waves are delocalized (spread out in space) (1) (2) (3) Waves can bend around small obstacle (1) and fan out from pinholes (2) while particles effuse from pinholes (3) Interference The Particle Nature of Light Blackbody radiation The photoelectric effect Atomic spectra Blackbody Radiation and the Quantization of Energy A B A. The interior of a cold ceramic-firing kiln approximates a blackbody, an object that absorbs all radiation falling on it and appears black. A hot kiln emits light characteristic of blackbody radiation. B Planck’s formula generates a curve that fits perfectly the changes in energy and intensity of light emitted by blackbody at different wavelength for a given temperature Planck’s Formula To find a physical explanation of blackbody Planck made a radical assumption that the hot, glowing object could emit (or absorb) only certain quantities of energy: E = nh Where E is the energy of the radiation, is its frequency, n is a positive integer (1, 2, 3 and so on) called a quantum number and h is a proportionality constant now called Planck’s constant and has value = 6,626x10-34 J.s The Photoelectric Effect and The Photon Theory of Light Current flow when monochromatic light of sufficient energy shines on a metal plate The photoelectric effect had certain features: the presence of a threshold frequency and the absence of a time lag Carrying Planck’s idea of packeted energy, Einstein proposed that light itself is particulate, occurring as quanta of electromagnetic energy, called photon In terms of Planck’s work we can say that each atom changes its energy whenever it absorbs or emits one photon, one “particle” of light, whose energy is fixed by its frequency Ephoton = hν = ∆Eatom Sampel Problem A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 12,0 cm. what is the energy of one photon of this microwave radiation? Calculate the energies of one photon of ultraviolet ( = 1x10-8 m), visible ( = 5x10- 7 m) and infrared ( = 1x10-4 m) light Solution E = h = hc/ = 1.66 x 10-24 J UV: E = hc/ = 2x10-17 J Visible: E = 4x10-19 m IR: E = 2x10-21 m Atomic Spectra Experimental key to atomic structure: analyze light emitted by high temperature gaseous elements. Experimental setup: spectroscopy Atoms emit a characteristic set of discrete wavelengths- not a continuous spectrum! atomic spectrum can be used as a "fingerprint" for an element hypothesis: if atoms emit only discrete wavelengths, maybe atoms can have only discrete energies an analogy The Bohr Model of the Hydrogen Atom Soon after the nuclear model was proposed, Niels Bohr suggested a model for the H atom that predicted the existence of line spectra The H atom has only certain allowable energy levels called stationary states The atom does not radiate energy while in one of its stationary states The atom changes to another stationary state (the electron moves to another orbit) only by absorbing or emitting a photon whose energy equals the difference in energy between two states: Ephoton = Estate A – E state B = hν where EA > EB . A spectral line results when a photon of specific energy is emitted as the electron moves from a higher energy state to a lower one. The Wave-Particle Duality of Matter and Energy Einstein proposed in his famous theory of relativity that matter and energy are alternate forms of the same entity This idea is embodied in his famous equation E = mc2, which relates the quantity of energy equivalent to a given mass and vice versa. This theory together with quantum theory have completely blurred the sharp divisions between matter (chunky and massive) and energy (diffuse and massles) that we see around us The Wave Nature of Electron and the Particle Nature of Photon According to Bohr’s theory, an atom has only certain allowable energy levels, however his assumption had no basis in physical theory In 1920s de Broglie proposed if energy is particlelike perhaps matter is wavelike. De Broglie reasoned that if electron have wavelike motion and are restricted to orbits of fixed radii, that would explain why they have only certain possible frequencies and energies Combining the equation the equation for mass-energy equivalence (E = mc2) with that for energy of a photon (E = hν = hc/λ) de Broglie derived an equation for the wavelength of any particle of mass m moving at speed u h mu According to this equation, matter behaves as thought it moves in a wave. The de Broglie wavelengths of several objects Substance Mass (g) Speed (m/s) (m) Slow electron 9 x 10-28 1.0 7 x 10-4 Fast electron 9 x 10-28 5.9 x 106 1 x 10-10 Alpha particle 6,6 x 10-24 1.5 x 107 7 x 10-15 One-gram mass 1.0 0.01 7 x 10-29 Baseball 142 25.0 2 x 10-34 Earth 6.0 x 1027 3.0 x 104 4 x 10-63 Sample Problems Calculate the de Broglie wavelength of an electron with a speed of 1.00x106 m/s (electron mass = 9.11x10-31 kg; h = 6.626x10-34 kg.m2/s) What is the speed of an electron that has a de Broglie wavelength of 100 nm? Nugraha, 85 kg speed 30 km/jam Answer = h/mu 7.27 x 10-10 m u = h/m 7.27 x 103 m/s The Quantum-Mechanical Model of the Atom Quantum Numbers of An Atomic Orbital 1. The principal quantum number (n) is a positive integer (1, 2, 3 and so forth). It indicates the relative size of the orbital and therefore the relative distance from the nucleus of the peak in the radial probability distribution plot 2. The angular momentum number (l) is an integer from 0 to n-1. it is related to the shape of the orbital and is sometimes called orbital-shape quantum number 3. The magnetic quantum number (ml) is an integer from –l through 0 to +l. it prescribes the orientation of the orbital in the space around the nucleus and is sometimes called the orbital-orientation quantum number The energy states and orbital of the atom are described with specific terms and associated with one or more quantum numbers: The atom’s energy levels or shells are given by n value; the smaller the n value the lower the energy level and the greater the probability of the electron being closer to the nucleus The atom’s levels contain sublevels or subshells which designate the orbital shape. Each sublevel has a letter designation: l = 0 is an s sublevel (sharp) l = 1 is a p sublevel (principal) l = 2 is a d sublevel (diffuse) l = 3 is an f sublevel (fundamental) Each allowed combination of n, l and ml values specific one of the atom’s orbital Shape of the s Orbital The p Orbital The d Orbital One of the seven f orbital

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posted: | 10/4/2012 |

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