Chapter 7: Quantum Theory and Atomic Structure. AP Chemistry. Late 1880s…physicists thought they knew everything…discouraged students from studying physics in college. CLASSICAL THEORY OF PHYSICS MATTER ENERGY -particulate -continuous -massive -wavelike. Background: WAVES. Waves.

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Chapter 7: Quantum Theory and Atomic Structure

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Late 1880s…physicists thought they knew everything…discouraged students from studying physics in college CLASSICAL THEORY OF PHYSICS MATTERENERGY -particulate-continuous -massive-wavelike

Waves A disturbance traveling through a medium by which energy is transferred from one particle of the medium to another without causing any permanent displacement of the medium itself.

Parts of A Wave node peak/crest trough wavelength distance between two consecutive peaks or troughs in a wave symbol: lambda, l units: meters (m) frequency the number of waves passing a point in a given amount of time symbol: nu, n units: cycles/sec, 1/sec, sec-1, Hertz (Hz)

PROBLEM: A dental hygienist uses x-rays (l= 1.00A) to take a series of dental radiographs while the patient listens to a radio station (l = 325cm) and looks out the window at the blue sky (l= 473nm). What is the frequency (in s-1) of the electromagnetic radiation from each source? (Assume that the radiation travels at the speed of light, 3.00x108m/s.) Sample Problem 7.1 Interconverting Wavelength and Frequency

Energy as a Wave Diffraction of Light Change in the directions and intensities of a group of waves after passing by an obstacle or through an aperture (slit) whose size is approximately the same as the wavelength of the waves

Figure 7.4 Different behaviors of waves and particles.

Energy as a PARTICLE • Heat a solid and it starts to glow • Why does the wavelength change with Temp? Hot coals ~1000 K Electric heating coil ~1500 K Lightbulb filament~2000 K

Max Planck (1903) - black body radiation Black body: a perfect absorber of radiation; object appears Black when cold and emits a temperature dependent spectrum of light Observations: Energy is gained and lost in whole numbers Intensity and frequency (color) of radiation depend on temperature Snow is a black body for IR radiation, but not for visible

Energy as a PARTICLE • Heat a solid and it starts to glow • Why does the wavelength change with Temp? • If an atom can only absorb certain wavelengths of energy, then it can only emit certain wavelengths Hot coals ~1000 K Electric heating coil ~1500 K Lightbulb filament~2000 K

Planck’s Quantum theory of EM waves Light energy is transmitted in discrete “packets” (photons) called quanta (singular is quantum) The energy of one quantum: E = h n h = Planck’s constant 6.63 x 10-34 J·s Niels Bohr and Max Planck at MIT

“Photoelectric Effect” Einstein (1905) When EM radiation above a certain frequency is shined on the device, an electric current registers on the meter As intensity increases, the current increases BUT – below the cutoff frequency, no current is obtained, even at very high intensities!! Conclusion: Photon is a “particle” of light with energy E=hn

PROBLEM: A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20cm. What is the energy of one photon of this microwave radiation? Sample Problem 7.2 Calculating the Energy of Radiation from Its Wavelength

Determination of the Structure of the Atom 1897- J.J. Thompson- Cathode Ray Tube Determined the charge/mass ratio of an electron. Suggested plum pudding model for atom 1911- Ernest Rutherford- Gold Foil Experiment Suggested presence of a positively charged nucleus Rutherford and Geiger.

Niels Bohr’s Model of the Atom (1913) • e- can only have specific (quantized) energy values • The e-’s energy correspond to orbits around the nucleus. Outer orbits have higher energy • light is emitted as e- moves from higher energy level to lower energy level Photon E=hn Ground State: n = Excited State: n Ionized: n = 1 >1 ∞

E = hn E = hn Problem – model does not work for atoms with more than 1 e- !!!

1 1 1 l n12 n22 Rydberg equation = R - R is the Rydberg constant = 1.096776 m-1 Three series of spectral lines of atomic hydrogen Figure 7.9 for the visible series, n1 = 2 and n2 = 3, 4, 5, ...

Figure 7.11 The Bohr explanation of the three series of spectral lines.

Figure B7.1 Flame tests strontium 38Sr copper 29Cu Figure B7.2 Emission and absorption spectra of sodium atoms.

Sample Problem 7.3 A hydrogen atom absorbs a photon of visible light and its electron enters the n = 4 energy level. Calculate • The change of energy of the atom, and • The wavelength (in nm) of the photon

Sample in compartment absorbs characteristic amount of each incoming wavelength. Computer converts signal into displayed data. Lenses/slits/collimaters narrow and align beam. Monochromator (wavelength selector) disperses incoming radiation into continuum of component wavelengths that are scanned or individually selected. Source produces radiation in region of interest. Must be stable and reproducible. In most cases, the source emits many wavelengths. Detector converts transmitted radiation into amplified electrical signal. Figure B7.3 The main components of a typical spectrophotometer

Louis De Broglie (1924) Q: Why is e- energy quantized? 1802 - T. Young - Light is a wave 1905 - A. Einstein - Light is also a particle 1899 – J.J. Thomson - e- is a particle - Maybe e- is also a wave!!!

only certain frequencies can work in a circle with a particular radius l = h/mu Wave-likeParticle-like PropertiesProperties u = velocity of e- m = mass of e-

Sample Problem 7.4 Find the deBroglie wavelength of an electron with a speed of 1.00x106m/s (electron mass = 9.11x10-31kg; h = 6.626x10-34 kg*m2/s).