SilberbergChap7ISM

SilberbergChap7ISM - CHAPTER 7 QUANTUM THEORY AND ATOMIC...

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CHAPTER 7 QUANTUM THEORY AND ATOMIC STRUCTURE The value for the speed of light will be 3.00 x 10 8 m/s except when more significant figures are necessary, in which cases, 2.9979 x 10 8 m/s will be used. 7.1 All types of electromagnetic radiation travel as waves at the same speed. They differ in their frequency, wavelength, and energy. 7.2 a) Figure 7.3 describes the electromagnetic spectrum by wavelength and frequency. Wavelength increases from left (10 –2 nm) to right (10 12 nm). The trend in increasing wavelength is: x-ray < ultraviolet < visible < infrared < microwave < radio waves . b) Frequency is inversely proportional to wavelength according to equation 7.1, so frequency has the opposite trend: radio < microwave < infrared < visible < ultraviolet < x-ray . c) Energy is directly proportional to frequency according to equation 7.2. Therefore, the trend in increasing energy matches the trend in increasing frequency: radio < microwave < infrared < visible < ultraviolet < x-ray . High- energy electromagnetic radiation disrupts cell function. It makes sense that you want to limit exposure to ultraviolet and x-ray radiation. 7.3 Evidence for the wave model is seen in the phenomena of diffraction and refraction. Evidence for the particle model includes the photoelectric effect and blackbody radiation. 7.4 In order to explain the formula he developed for the energy vs. wavelength data of blackbody radiation, Max Planck assumed that only certain quantities of energy, called quanta, could be emitted or absorbed. The magnitude of these gains and losses were whole number multiples of the frequency: Δ E = nh ν . 7.5 Radiation (light energy) occurs as quanta of electromagnetic radiation, where each packet of energy is called a photon. The energy associated with this photon is fixed by its frequency, E = h . Since energy depends on frequency, a threshold (minimum) frequency is to be expected. A current will flow as soon as a photon of sufficient energy reaches the metal plate, so there is no time lag. 7.6 a) Frequency: C < B < A b) Energy: C < B < A c) Amplitude: B < C < A d) Since wave A has a higher energy and frequency than B, wave A is more likely to cause a current. e) Wave C is more likely to be infrared radiation since Wave C has a longer wavelength than B. 7.7 Plan: Wavelength is related to frequency through the equation c = λ . Recall that a Hz is a reciprocal second, or 1/s = s –1 . Assume that the number “960” has three significant figures. Solution: c = λ λ (m) = c ν = () 8 3 3.00 x 10 m/s 10 Hz s 950. kHz 1kHz Hz ⎛⎞ ⎜⎟ ⎝⎠ 1 = 315.8 = 316 m λ (nm) = c ν = 8 9 31 3.00 x 10 m/s 1 nm 10 m 10 Hz s 950. kHz 1 kHz Hz = 3.158 x 10 11 = 3.16 x 10 11 nm 7-1
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λ (Å) = c ν = () 8 10 31 3.00 x 10 m/s 1 Å 10 m 10 Hz s 950. kHz 1 kHz Hz ⎛⎞ ⎝⎠ ⎜⎟ = 3.158 x 10 12 = 3.16 x 10 12 Å 7.8 Wavelength and frequency relate through the equation c = λν . Recall that a Hz is a reciprocal second, or 1/s = s –1 .
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SilberbergChap7ISM - CHAPTER 7 QUANTUM THEORY AND ATOMIC...

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