Chapter 6
Q. 6.1
You sit in your back yard on a warm summer evening watching the red sky (λ = 625 nm) at sunset and listening to music from your CD player. The laser in the latter has frequency 3.84 × 10^{14} s^{-1}.
(a) What is the frequency of the radiation from the red sky?
(b) What is the wavelength of the laser in nm?
| ANALYSIS | |
| wavelength of the sky’s red color (625 nm) frequency of the laser (3.84 × 10^{14} s^{-1}) |
Information given: |
| speed of light (2.998 × 10^{8} m/s) meter to nanometer conversion factor |
Information implied: |
| frequency of the sky’s radiation laser’s wavelength in nm |
Asked for: |
STRATEGY
1. Recall the Greek letters used as symbols for frequency (v) and wavelength (λ).
2. Use Equation 6.1 to relate frequency and wavelength.
λv = c (6.1)
3. Convert nm to m (a) and m to nm (b).
Step-by-Step
Verified Solution
| 625 nm × \frac{1 × 10^{-9} m}{1 nm} = 625 × 10^{-9} m
v = \frac{c}{λ} = \frac{2 .998 × 10^{8} m/s}{625 × 10^{-9} m} = 4.80 × 10^{14} s^{-1} |
(a) Wavelength in meters
Frequency |
| λ = \frac{c}{v} = \frac{2 .998 × 10^{8} m/s}{3.84 × 10^{14}s^{-1}} = 7.81 × 10^{-7} m
7.81 × 10^{-7} m × \frac{1 nm}{1 × 10^{-9} m} = 781 nm |
(b) Wavelength
Wavelength in nm |