To find the frequency of light given its wavelength and speed, we can use the formula:
[tex]\[ \text{frequency} = \frac{\text{speed of light}}{\text{wavelength}} \][/tex]
Given:
- Wavelength [tex]\( \lambda = 450 \, \text{nm} = 450 \times 10^{-9} \, \text{m} = 4.50 \times 10^{-7} \, \text{m} \)[/tex]
- Speed of light [tex]\( c = 3.0 \times 10^8 \, \text{m/s} \)[/tex]
Let's substitute these values into the formula:
[tex]\[ \text{frequency} = \frac{3.0 \times 10^8 \, \text{m/s}}{4.50 \times 10^{-7} \, \text{m}} \][/tex]
Now, perform the division:
[tex]\[ \text{frequency} = \frac{3.0 \times 10^8}{4.50 \times 10^{-7}} \][/tex]
[tex]\[ \text{frequency} \approx 666666666666666.8 \, \text{Hz} \][/tex]
This result is approximately [tex]\(6.67 \times 10^{14} \, \text{Hz}\)[/tex], which corresponds to Option C.
Therefore, the frequency of the light is:
[tex]\[ \boxed{6.67 \times 10^{14} \, \text{Hz}} \][/tex]
The correct answer is:
C. [tex]\(6.67 \times 10^{14} \, \text{Hz}\)[/tex]
