To determine the frequency of the light wave, we can use the fundamental relationship between speed, frequency, and wavelength, which is given by the equation:
[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]
Here, we are given the speed of light and the wavelength:
- Speed of light, [tex]\( c = 3.0 \times 10^8 \)[/tex] meters/second
- Wavelength, [tex]\( \lambda = 7.0 \times 10^{-7} \)[/tex] meters
We need to solve for the frequency [tex]\( f \)[/tex]. Rearranging the equation to solve for frequency, we get:
[tex]\[ f = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]
Substituting the given values into the equation:
[tex]\[ f = \frac{3.0 \times 10^8 \text{ m/s}}{7.0 \times 10^{-7} \text{ m}} \][/tex]
When we divide these values, we get:
[tex]\[ f = 4.2857142857142856 \times 10^{14} \text{ Hz} \][/tex]
To select the correct answer from our options, let's compare our result with the given choices:
A. [tex]\( 2.5 \times 10^{-14} \)[/tex] Hz
B. [tex]\( 4.3 \times 10^{14} \)[/tex] Hz
C. [tex]\( 1.7 \times 10^{-14} \)[/tex] Hz
D. [tex]\( 5.1 \times 10^{-14} \)[/tex] Hz
The result [tex]\( 4.2857142857142856 \times 10^{14} Hz \)[/tex] is very close to [tex]\( 4.3 \times 10^{14} Hz \)[/tex], which corresponds to option B.
Therefore, the correct answer is:
B. [tex]\( 4.3 \times 10^{14} \)[/tex] hertz
