This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CHAPTER 7 QUANTUM THEORY AND THE ELECTRONIC STRUCTURE OF ATOMS 7.7 (a) 8 6 13 3.00 10 m/s 3.5 10 m 8.6 10 /s = = = = 3 3.5 10 nm c (b) 8 14 9 3.00 10 m/s 5.30 10 /s 566 10 m = = = = 14 5.30 10 Hz c 7.8 (a) Strategy: We are given the wavelength of an electromagnetic wave and asked to calculate the frequency. Rearranging Equation (7.1) of the text and replacing u with c (the speed of light) gives: = c Solution: Because the speed of light is given in meters per second, it is convenient to first convert wavelength to units of meters. Recall that 1 nm = 1 10 9 m (see Table 1.3 of the text). We write: 9 9 7 1 10 m 456 nm 456 10 m 4.56 10 m 1 nm = = Substituting in the wavelength and the speed of light (3.00 10 8 m/s), the frequency is: 8 7 m 3.00 10 s or 4.56 10 m = = = 14 1 14 6.58 10 s 6.58 10 Hz c Check: The answer shows that 6.58 10 14 waves pass a fixed point every second. This very high frequency is in accordance with the very high speed of light. (b) Strategy: We are given the frequency of an electromagnetic wave and asked to calculate the wavelength. Rearranging Equation (7.1) of the text and replacing u with c (the speed of light) gives: = c Solution: Substituting in the frequency and the speed of light (3.00 10 8 m/s) into the above equation, the wavelength is: 8 9 m 3.00 10 s 0.122 m 1 2.45 10 s = = = c CHAPTER 7: QUANTUM THEORY AND THE ELECTRONIC STRUCTURE OF ATOMS 195 The problem asks for the wavelength in units of nanometers. Recall that 1 nm = 1 10 9 m. 9 1 nm 0.122 m 1 10 m = = 8 1.22 10 nm 7.9 Since the speed of light is 3.00 10 8 m/s, we can write 8 8 1.61 km 1000 m 1 s (1.3 10 mi) 1 mi 1 km 3.00 10 m = 2 7.0 10 s Would the time be different for other types of electromagnetic radiation? 7.10 A radio wave is an electromagnetic wave, which travels at the speed of light. The speed of light is in units of m/s, so lets convert distance from units of miles to meters. (28 million mi = 2.8 10 7 mi) 7 1 1.61 km 1000 m ? distance (m) (2.8 10 mi) 4.5 10 m 1 mi 1 km = = Now, we can use the speed of light as a conversion factor to convert from meters to seconds ( c = 3.00 10 8 m/s). 10 2 8 1 s (4.5 10 m) 1.5 10 s 3.00 10 m = = = ? min 2.5 min 7.11 8 2 1 3.00 10 m/s 3.26 10 m 9192631770 s = = = = 7 3.26 10 nm c This radiation falls in the microwave region of the spectrum. (See Figure 7.4 of the text.) 7.12 The wavelength is: 7 1 m 6.05780211 10 m 1,650,763.73 wavelengths = = 8 7 3.00 10 m/s = 6.05780211 10 m = = 14 1 4.95 10 s c 7.15 34 8 9 (6.63 10 J s)(3.00 10 m/s) 624 10 m = = = = 19 3.19 10 J hc h E 7.16 (a) Strategy: We are given the frequency of an electromagnetic wave and asked to calculate the wavelength....
View
Full
Document
This homework help was uploaded on 04/21/2008 for the course CHEM 112 taught by Professor Heglund during the Spring '08 term at SDSMT.
 Spring '08
 Heglund
 Electron

Click to edit the document details