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## 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).

## 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