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The Quantum-Mechanical Model of the Atom

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  1. The Quantum-Mechanical Model of the Atom

  2. Atoms and Energy All energy is either kineticenergy (the energy of motion), or potential energy (energy based on position). In chemical systems, thermal energy is of interest as particles move, collide, and exchange energy. In individual atoms, electrostatic energy, arising from the attraction or repulsion of charges is of interest.

  3. Coulomb’s Law Attraction or replusion between charged particles can be calculated using Couomb’s Law: E = (Qae)(Qbe) α QaQb 4πεorab rab Qa and Qb = charges on the particles e= charge of an electron (-1.602 x 10-19C) 4πεo=permittivity of vacuum (1.1127 x 10-10J-1C2m-1) rab = distance between the particles

  4. Electrostatic Energy With oppositely charged particles, the energy is negative, indicating attraction between the particles and a lowering of potential energy as the particles are closer to each other. E α (QaQb)÷ d

  5. Electrostatic Energy E α (QaQb)/d It is important to note that the attraction between opposite charges increases dramatically as the magnitude of the charges on the particles increases.

  6. Units of Energy There are many different units used for energy depending on the application. The SI unit for energy is joules (J), which is the energy exerted when a force of 1 newton over a distance of 1 meter. A newton (N) is a force of 1kg (m/s2). Although this unit is related to kinetic energy (a force acting over a distance), it can be used for other types of energy.

  7. Matter and Energy By 1900, physicists thought that the nature of energy and matter was well understood and distinct. Matter, a collection of particles, has mass and a defined position in space. Radiant (light) energy, as waves, is massless and delocalized. It was also believed that particles of matter could absorb or emit any energy, without restriction.

  8. Matter and Energy After Rutherford, Geiger and Marsden proposed the nuclear model of the atom, scientists focused on how the electrons are arranged around the nucleus. Since electrons could not be observed directly, scientists studied the light that matter emits when it is stimulated by heat or an electric discharge.

  9. Atomic Spectroscopy The study of the light emitted or absorbed by matter is a branch of chemistry called spectroscopy. Atomic spectroscopy allows scientists to understand the nature of the electrons in atoms. Molecular spectroscopy provides information about the bonds in molecules.

  10. Electromagnetic Radiation Early atomic scientists studied the interaction of matter with electromagnetic radiation, or light. Electromagnetic radiation, or radiant energy, includes visible light, infrared, micro and radio waves, and X-rays and ultraviolet light.

  11. Electromagnetic Radiation Light consists of oscillating electric and magnetic fields that travel through space at the rate of 3 x 108m/s. The oscillating fields interact with electrons in the atom.

  12. Electromagnetic Radiation This drawing represents a “snapshot” of an electro-magnetic wave at a given instant.

  13. Electromagnetic Radiation Electromagnetic radiation travels in waves. The waves of radiant energy have three important characteristics: 1. Wavelength - λ - (lambda) 2. Frequency – ν – (nu) 3. Speed – c – the speed of light

  14. Wavelength Wavelength, λ, is the distance between two adjacent peaks or troughs in a wave. The units may range from picometers to kilometers depending upon the energy of the wave.

  15. Frequency Frequency, ν, is the number of waves (or cycles) that pass a given point in space per second. The units are cycles/s, s-1 or hertz (Hz).

  16. The Speed of Light All electromagnetic radiation travels at the same speed. The speed of light ( c ) is: c = 2.9979 x 108 m/s

  17. Wavelength and Frequency Wavelength and frequency are inversely related. That is, waves with a low frequency have a long wavelength. Waves with a high frequency have short wavelengths.

  18. Electromagnetic Radiation The relationship between wavelength and frequency is: λν = c

  19. Properties of Light - Amplitude

  20. Diffraction Waves of electromagnetic radiation are bent or diffracted with they a passed through an obstacle or a slit with a size comparable to their wavelength.

  21. Interference Patterns

  22. The Failure of Classical Physics Observations of the behavior of sub-atomic particles in the early 1900s could not be predicted or explained using classical physics. Very small particles such as electrons appear to interact with electromagnetic radiation (light) differently than objects we can see and handle.

  23. Black Body Radiation Physicists focused on interactions between light (electromagnetic radiation) and matter to try to better understand the nature of the atom. When objects are heated, they emit light in relation to their temperature. Iron rods glow red, and will glow yellow at higher temperatures.

  24. Black Body Radiation Classical physics, when applied to black body radiation, predicted that the intensity of the radiation emitted would dramatically increase at shorter and shorter wavelengths. The result was that any hot body should emit intense UV radiation, and even x-rays. Even a human body at 37oC would glow in the dark. This discrepancy between theory and observation is called “The Ultraviolet Catastrophe.”

  25. The Ultraviolet Catastrophe The failure of classical physics is seen in the shorter wavelength ultraviolet region

  26. Planck & Black Body Radiation Max Planck (1858-1947) studied the radiation emitted by objects heated until they glowed. In order to explain the observations, he proposed (in 1900) that the energy emitted was not continuous, but instead was released in multiples of hν. h is known as Planck’s constant.

  27. Planck & Black Body Radiation ∆E = nhν where n=integer ν = frequency h = 6.626 x 10-34 J-s Planck’s work showed that when matter and energy interact, the energy is quantized, and can occur only in discrete units or bundles with energy of hν.

  28. Planck & Black Body Radiation ∆E = nhν Each packet or bundle of energy is called a quantum. A fraction of a quantum is never emitted. A quantum is the smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation.

  29. Planck’s Law Planck’s approach shows good agreement between the observed spectrum (in blue) and the calculated values (in red).

  30. Planck’s Law Planck’s law was based on empirical data. He found a mathematical relationship that fits the observations. It is important to note that Planck did not explain the reason for the relationship. The concept of energy being quantized rather than continuous was quite revolutionary.

  31. Planck & Black Body Radiation Planck received the Nobel Prize for his work in 1918 (at the age of 42).

  32. Einstein – Photoelectric Effect Albert Einstein (1879-1955) won a Nobel Prize for his explanation of the photoelectric effect. When light of sufficient energy strikes the surface of a metal, electrons are emitted from the metal surface. Each metal has a characteristic minimum frequency, νo , called the threshold frequency, needed for electrons to be emitted.

  33. The Photoelectric Effect

  34. Observations 1. No electrons are emitted if the frequency of light used is less than νo, regardless of the intensity of the light. 2. For light with a frequency≥ νo , electrons are emitted. The number of electrons increases with the intensity of the light. 3. For light with a frequency > νo , the electrons are emitted with greater kinetic energy.

  35. Explanation Einstein proposed that light is quantized, consisting of a stream of “particles” called photons. If the photon has sufficient energy, it can “knock off” an electron from the metal surface. If the energy of the photon is greater than that needed to eject an electron, the excess energy is transferred to the electron as kinetic energy.

  36. The Photoelectric Effect Ephoton= hν = hc/λ If incident radiation with a frequency νi is used: KEelectron = hνi -hνo = ½ mv2 The kinetic energy of the electron equals the energy of the incident radiation less the minimum energy needed to eject an electron.

  37. The Photoelectric Effect The frequency hνo is the minimum energy needed to eject an electron from a specific metal. This energy is called the binding energy of the emitted electron. Binding energy is often expressed in electron volts (eV), with 1 eV = 1.602 x 10–19 J.

  38. Particle-Wave Duality Einstein’s work suggested that the incident photon behaved like a particle. If it “hits” the metal surface with sufficient energy (hνi), the excess energy of the photon is transferred to the ejected electron. In the atomic scale, waves of radiant energy have particle-like properties.

  39. Particle-Wave Duality Einstein also combined his equations: E=mc2 with Ephoton= hc/λ to obtain the “mass” of a photon: m= m= hc/λ E = c2 c2 h λc

  40. Albert Einstein

  41. Particle-Wave Duality The apparent mass of radiant energy can be calculated. Although a wave lacks any mass at rest, at times, it behaves as if it has mass. Einstein’s equation was confirmed by experiments done by Arthur Compton in 1922. Collisions between X-rays and electrons confirmed the “mass” of the radiation.

  42. Particle-Wave Duality Arthur Compton attempted to study the collision of a light quantum with an electron moving freely through space. However, creating a collision between a beam of light and a beam of electrons isn’t feasible, since it would take an extremely long time for such a collision to occur.

  43. Arthur Compton Compton solved this problem by using extremely high energy x-rays to bombard small atoms. Since the energy of the radiation was so high, the electrons in the atoms were viewed as “free” by comparison. Compton viewed the collision as if between two elastic spheres, and perfectly predicted the scattering of the x-rays and the decrease in frequency as a result of the collision.

  44. Arthur Compton Compton received the Nobel prize in 1927.

  45. Emission Spectrum of Hydrogen When atoms are given extra energy, or excited, they give off the excess energy as light as they return to their original energy, or ground state. H2 Hg He

  46. Emission Spectrum of Hydrogen Scientists expected atoms to be able to absorb and emit a continuous range of energies, so that a continuous spectrum of wavelengths would be emitted.

  47. Emission Spectrum of Hydrogen A continuous spectrum in the visible range, would look like a rainbow, with all colors visible. Instead, hydrogen, and other excited atoms emit only specific wavelengths of light as they return to the ground state. A line spectrum results.

  48. Emission Spectrum of Hydrogen