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Unformatted text preview: Chapter 6: Electronic Structure of Atoms Chapter Waves Waves To understand the electronic structure To of atoms, one must understand the nature of electromagnetic radiation. nature The distance between corresponding The points on adjacent waves is the wavelength (λ ). wavelength The number of waves passing a given The point per unit of time is the point frequency (ν ) frequency For waves traveling at the same For velocity, the longer the wavelength, the smaller the frequency. smaller Waves Waves Electromagnetic Radiation Electromagnetic All electromagnetic radiation travels at the same All velocity: the speed of light (c), 3.00 × 108 m/s. velocity: ), Therefore: c = λν λν The Nature of Energy The The wave nature of light The does not explain how an object can glow at high temperatures. temperatures. Max Planck explained it Max by assuming that energy comes in packets called quanta. quanta The Nature of Energy The Einstein used quanta Einstein quanta explain the photoelectric effect, photoelectric And stated that And energy is energy proportional to frequency (ν ) : frequency E = hν where h is where Planck’s constant: Planck’s 6.63 × 10−34 J-s. The Nature of Energy The If the wavelength (λ ) of If light is known, then the energy in one photon energy (packet of that light) can be calculated: be c = λν λν E = hν ν= λ / c E = h•λ / c λ/ h is Planck’s constant The Nature of Energy The Another mystery Another involved the emission spectra observed from spectra energy emitted by atoms and molecules. atoms The Nature of Energy The Light emitted by atoms and molecules does Light not form a continuous spectrum, as with a white light source. Instead a line spectrum of line discrete wavelengths is observed. discrete
Na H continuous spectrum line spectra The Nature of Energy The
Niels Bohr adopted Planck’s Niels assumption and explained these phenomena in this way: these Electrons in an atom can Electrons only occupy certain orbits (corresponding to certain energies). energies). The Nature of Energy The
Niels Bohr adopted Planck’s assumption Niels and explained these phenomena in this way: way: Electrons in permitted Electrons orbits have specific, “allowed” energies; these energies will not not be radiated from the atom. atom. The Nature of Energy The
Niels Bohr adopted Planck’s Niels assumption and explained these phenomena in this way: these Energy is only absorbed or Energy absorbed emitted in such a way as to emitted move an electron from one “allowed” energy state to energy another; the energy is defined by E = hν The Nature of Energy The
The energy absorbed or emitted The from the process of electron promotion or demotion can be calculated by the equation: calculated ∆ E = -RH ( 1 1 - ni2 nf2 ) where RH is the Rydberg where constant, 2.18 × 10−18 J, and ni and nf are the initial and final final energy levels of the electron. energy The Wave Nature of Matter The Louis de Broglie proposed that: Louis if light can have material properties, matter should exhibit wave properties. matter He demonstrated that the relationship He between mass and wavelength was: between λ= h mv The Uncertainty Principle Heisenberg showed that the more Heisenberg precisely the momentum of a particle is known, the less precisely is its position known: known: h (∆ x) (∆ mv) ≥ 4π In many cases, our uncertainty of the In whereabouts of an electron is greater than the size of the atom itself! than Quantum Mechanics Quantum Erwin Schrödinger Erwin developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. incorporated. It is known as quantum It mechanics. mechanics. Quantum Mechanics Quantum The wave equation is The designated with a lower case Greek psi (ψ ). psi The square of the wave The equation, ψ 2, gives a probability density probability map of where an electron electron has a certain statistical likelihood of being at any given instant in time. given Quantum Numbers Quantum Solving the wave equation gives a Solving set of wave functions, or orbitals, orbitals and their corresponding energies. and Each orbital describes a spatial Each distribution of electron density. distribution An orbital is described by a set of An three quantum numbers. quantum Principal Quantum Number, n The principal quantum number, n, The principal describes the energy level on energy which the orbital resides. which The values of n are integers ≥ 0. The ...
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