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Chapter 7

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University of Toronto Mississauga
Judith C Poe

Chapter 7: Quantum Theory and Atomic Structure 7.1: The Nature of Light  Electromagnetic Radiation: consists of energy propagated by electric and magnetic fields that increase and decrease in intensity as they move through space. (ex. visible light, x-rays, and microwaves) The Wave Nature of Light The wave properties of electromagnetic radiation are described by three variables and one constant: 1. Frequency (v, Greek nu): the frequency of a wave is the number of cycles it undergoes per second, -1 expressed by the unit 1/second (s , also called a hertz (Hz)) 2. Wavelength (λ): the wavelength is the distance b/w any point on a wave and the corresponding point of the next crest (or trough) of the wave (the distance a wave travels during one cycle).  uses units of meters, or nanometers (10 m), picometers (pm, 10 -12m) or the non-SI unit angstroms 3. 3. Speed: the speed of a wave is the distance it moves per unit time (m/s), the product of its frequency (cycles per second) and wavelength (meters per cycle)  In a vacuum, electromagnetic radiation moves at 3 x 10 m/s (the speed of light, c) o c = v x λ  Since the product of v and λ is a constant, they have a reciprocal relationship- radiation with a high frequency has a short wavelength and vice versa. o v  λ o v  λ 4. Amplitude: the amplitude of a wave is the height of the crest or depth of a trough. The amplitude is related to the intensity of radiation, or its brightness in the case of visible light. The Electromagnetic Spectrum  All waves in the spectrum travel at the same speed through a vacuum but differ in frequency and, therefore, wavelength.  The spectrum is a continuum of radiant energy so each region meets the next.  Light of a single wavelength is called monochromatic  Light of many wavelengths is polychromatic  Ranges from very long radio waves to very short gamma rays and includes the visible region b/w wavelengths 750nm (red) and 400nm (violet). The Distinction Between Energy and Matter 1. Refraction and dispersion: light of a given wavelength travels at different speeds through various transparent media. Therefore, when a light wave passes from one medium to another, the speed of the wave changes (refraction). If a wave strikes a boundary b/w media at any angle other than 90, the change in speed causes a change in direction, and the wave continues at a different angle. In dispersion, white light separates into its component colors when it passes through a prism b/c each incoming wave is refracted at a slightly different angle. 2. Diffraction and Interference: When a wave strikes the edge of an object, it bends around it (diffraction). When light passes sharp edges or goes through narrow slits the rays are deflected and produce fringes of light and dark bands. When waves of light pass through two adjacent slits, the nearby emerging circular waves interact through the process of interference. The combination of two or more electromagnetic waveforms to form a resultant wave in which the displacement is either reinforced or canceled. If the crests of the waves coincide (in phase), they interfere constructively-the amplitudes add together to form a brighter region. If crest coincide with the troughs (out of phase), they interfere destructively-the amplitudes cancel to form a darker region. The Particle Nature of Light Blackbody Radiation and the Quantum Theory of Energy Observation: when a solid object is heated to about 1000 K, it begins to emit visible light. At about 1500K, the light is brighter and more orange. These changes in intensity and wavelength of emitted light as an object is heated are characteristic of blackbody radiation, light given off by a hot blackbody. Explanation: the quantum theory, Planck developed a formula that fit the data perfectly: the object could emit (or absorb) only certain quantities of energy: E = nhv where E is the energy of the radiation, v is the frequency, n is a positive integer called a quantum number and h is Planck’s Constant: -34 h = 6.62606876 x 10 J-s  Since hot objects emit a certain amount of energy, the energy must be emitted by the atoms in certain quantities.  The energy of an atom is quantized; it occurs in fixed quantities rather than being continuous.  Each change in atom’s energy occurs when the atom absorbs or emits one or more “packets” of energy called a quantum.  A quantum energy is equal to hv. Thus, an atom changes its energy state by emitting (or absorbing) one or more quanta and the energy of the emitted (or absorbed) radiation is equal to the difference in the atom’s energy states: o ΔE atom= Eemitted (or absorbed) radiation The Photoelectric Effect and the Photon Theory of Light Observation: the photoelectric effect. When monochromatic light of sufficient frequency shines on a metal plate, a current flows. It was thought that the current arises b/c of light transfers energy that frees electrons from the metal surface. However there were two confusing features: 1. Presence of a threshold frequency: for current to flow, the light shining on the metal must have a minimum, or threshold, frequency, and different metals have different minimum frequencies. But, the wave theory associates the energy of the light with the amplitude not the frequency. Thus, the theory predicts that an electron would break free when it absorbed enough energy from light of any color. 2. Absence of a time lag: current flows the moment light of the minimum frequency shines on the metal, regardless of the light’s intensity. The wave theory predicts that w. dim light there would be a time lag b/f the current flows b/c the electrons would have to absorb enough energy to break free. Explanation: the photon theory. Einstein proposed that light itself it particulate, quantized into tiny “bundles” of energy, later called photons. Each atom changes its energy, ΔE atom, when it absorbs or emits one photon, one “particle” of light, whose energy is related to its frequency, not its amplitude. E photon hv = ΔEatom 1. Why there is threshold frequency: a beam of light consists of a lot of photons. The intensity (brightness) is related to the number of photons, but not to the energy of each. Therefore, a photon of a certain minimum must be absorbed to free an electron from the surface. 2. Why there is no time lag: an electron breaks free when it absorbs a photon of enough energy; it can’t break free by “saving up” energy from several photons. The current is weak in dim light b/c fewer photons of enough energy can free fewer electrons per unit time, but some current flows as soon as light of sufficient energy (frequency) strikes the metal. 7.2: Atomic Spectra Line Spectra and the Rydberg Equation  when light from electrically excited gaseous atoms passes through a slit and is refracted by a prism, it doesn’t create a continuous spectrum but creates a line spectrum: a series of fine lines at specific frequencies separated by black spaces Features of the Rydberg Equation:  the Rydberg equation predicts the position and wavelength of any line in a given series: where: λ is the wavelength of the line n and n are positive integers 1 2 7 -1 R is the Rydberg constant = 1.096776 x 10 m Problems with Rutherford’s Nuclear Model  A positive nucleus and a negative electron attract each other, and for them to stay apart, the kinetic energy of the electron’s motion must counterbalance the potential energy of attraction.  The laws of classical physics sat that a negative particle moving in a curving path around a positive particle must emit radiation and thus lose energy. If this happened the atom would collapse The Bohr Model of the Hydrogen Atom Postulates: 1. The H atom has only certain energy levels, which Bohr called stationary states. Each state is associated w. a fixed circular orbit of the electron around the nucleus, the higher the energy level, the farther the orbit is from the nucleus. 2. The atom doesn’t radiate energy while in one of its stationary states. Even though it violated the principle of classical physics, the atom doesn’t change energy while the electron moves within the orbit. 3. The atom changes to another stationary state (the electrons moves to another orbit) only by absorbing or emitting a photon. The energy of the photon (hv) equals the difference in the energies of the two states.  E photon ΔE atom= EfinalEinitialhv Features:  Quantum numbers and electron orbit: the quantum number n is a positive integer associated w. the radius of an electron orbit, which is directly related to the electron’s energy: o the lower the n value, the smaller the radius of the orbit, and the lower the energy level  Ground State: when the electron is in the first orbit it is closest to the nucleus, and the H atom is in its lowest energy level called the ground state.  Excited States: if the electron is in any orbit further from the nucleus, the atom is in an excited state. o n = 2 is the first excited state  Absorption: if an H atom absorbs a photon whose energy equals the difference b/w lower and higher energy levels, the electron moves to the outer orbit  Emission: if an H atom in a higher energy level returns to a lower energy level, the atom emits a photon whose energy equals the difference b/w the two levels. How the Model Explains Line Spectra  a spectral line results b/c a photon of specific energy is emitted, the emission occurs when the electron moves an orbit closer to the nucleus as the atom’s energy changes from a higher state to a lower one.  an atomic spectrum is not continuous b/c the atom’s energy is not continuous but rather has only certain states.  when electrons drop from outer orbits to n=3, the emitted photons create the infrared series of lines.  the visible series is a drop from outer orbits to n=2  the ultraviolet series arises when electrons drop to n=1 Limitations of the Model  only predicts the Hydrogen spectrum, fails to predict the spectrum of any other atom b/c it is an one electron model so it works for hydrogen and other 1 electron species  it fails for other b/c of electron-electron repulsio
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