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##### Electronic Structure of Atoms

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**The Wave Nature of Light**• Electromagnetic radiation (EM radiation) carries energy through space. • All EM radiation travels through a vacuum at 3.00 x 108 m/s (speed of light). You must memorize this number!!!**Parts of a Light Wave**Wave peak • Wavelength (): distance between two wave peaks (m) • Frequency (): number of waves per second. Units of Hertz (Hz) or reciprocal seconds (s-1). 1Hz = 1 s-1 • Amplitude: half thedistance from the wave peak to the trough. trough amplitude**What Is The Relationship Between Wavelength and Frequency?**c = c = speed of light = 3.00 x 108m/s = wavelength (m) = frequency (s-1) nd are inversely proportional. As wavelength gets shorter, the frequency gets higher; as wavelength gets longer, the frequency gets lower.**Calculations With Wavelength and Frequency**• What is the wavelength of radiation with a frequency of 7.32 x 1019 s-1? • What is the frequency of radiation having a wavelength of 754 nm?**Planck and Black-body Radiation**• Max Planck studied how temperature and EM radiation are related. • He assumed energy can be emitted or absorbed by atoms only in discrete “chunks” of some minimum size. • Quantum (“fixed amount”) is the smallest quantity of energy that can be absorbed or emitted as EM radiation.**Planck’s Equation**E = h E = energy of a single quantum (J) h = Planck’s constant: (6.626 x 10-34 J-s) = frequency (s-1)**Using the Energy Equation**Calculate the energy of light with a frequency of 6.00 x 1014 s-1.**More Energy Calculations**Calculate the wavelength of light having an energy of 2.54 x 10-20 J.**Planck’s Quantum Theory**• Energy is always absorbed or emitted in whole number multiples of hv (hv, 2hv, 3hv, etc.) • Allowed energies are quantized = restricted to certain values. • Planck’s theory applies best to small objects like electrons. • Planck is “Father of Quantum Physics.”**Einstein and Photons**• Radiant energy striking a metal surface is a stream of tiny energy packets called photons. • Photons behave like particles. • The energy of a photon equals the frequency of light in which it travels. Ephoton = hv or Ephoton = hc/λ Radiant energy is quantized!**Einstein Discovered the Photoelectric Effect**• When a photon strikes a metal, it may transfer its energy to an electron. • If the photon has enough energy to meet the electron’s specific energy requirement, the electron is emitted from the metal. • Each metal has its own minimum energy needs to excite its electrons. • This is called threshold energy. • Not enough energy = no electron emission!**Radiant Energy and Spectra**• The radiant energy from a laser emits a single wavelength (monochromatic) but most common radiation sources such as light bulbs and stars emit many different wavelengths. A spectrum is produced when polychromatic radiation is separated into its different wavelengths. A spectrum producing light of all colors is called a continuous spectrum.**Line Spectra**• Not all radiation sources produce a continuous spectrum. • When gases are placed in a tube under reduced pressure with high voltage, different colors of light are emitted. • When light from such tubes are passed through a prism, only lines of a few wavelengths are seen. • The colored lines are separated by black regions which correspond to absent wavelengths. • These spectra are called line spectra.**Bohr’s Atomic Model Based On Spectral Lines**Here is Bohr’s model of the hydrogen atom with electron movement corresponding to observed spectral lines.**Niels Bohr’s Atomic Model**• Bohr based his atomic model on the hydrogen atom with only one electron. • He assumed that the electron moves in a circular orbit around the nucleus. • According to classical physics, the electron should lose energy as it orbits and spiral into the nucleus. • Since the electron does not spiral into the nucleus, the old laws of physics are inadequate to describe the atom.**Bohr’s Three Postulates**• Only orbits of certain radii with certain definite energies are permitted for electrons in an atom. • An electron in a permitted orbit has a specific energy and is in an “allowed” energy state. It will not radiate energy and spiral into the nucleus. • Energy is only emitted or absorbed by an electron as it changes from one energy state to another. Energy is emitted or absorbed as a photon (E = h).**Energy States of the Hydrogen Atom**• Integer n (values 1 to ) is called principalquantum number. • Each n value corresponds to a different orbit. • The radius of the orbit gets bigger as n increases. • n = 1 is closest to the nucleus; succeeding n’s get farther away. • The spacing between the n levels are uneven; the greatest spacing occurs between the nucleus and n = 1. • Successive n levels are scrunched closer together. • Lowest energy state is the ground state; a higher energy state is an excited state.**Significance of Bohr Model**• Works best for hydrogen atom; does not work well with mutli-electron atoms. • Treats the electron as a small particle. • Introduces distinct energy levels described by quantum numbers. • Says that energy is needed to move an electron from one energy level to another.**Is Radiation a Particle or a Wave?**• Depending on experiment, radiation has either wavelike or particle-like (photon) character. • Given that wavelengths of radiation have particle-like character, can matter (made up of particles) have wavelike character?**Wave-Particle Duality**• Louis de Broglie theorized that an electron in its movement about the nucleus does have a wavelength associated with it. • Wave-particle duality: electrons have both particle and wave characteristics.**Heisenberg’s Uncertainty Principle**It is impossible to know simultaneously both the exact momentum of an electron and its exact location. Leads to a new atomic model in which the energy of an electron is known but its location is described in terms of mathematical probabilities.**Quantum Mechanical Model**• Erwin Schrödinger uses an equation to incorporate the wavelike and particle-like qualities of electrons. • This became the basis for the quantum mechanical(wave mechanical, electron cloud) model.This is our current atomic model!! • Schrödinger’s work deals with probabilities.**Schrodinger’s Model**• Probability density = the probability that an electron will be found at a given location. • Node = a location where there is no probability of finding an electron. • Electron density = region where there is a high probability of finding an electron.