Light having a wavelength of [tex][tex]$450 \, \text{nm} \left(4.50 \times 10^{-7} \, \text{m} \right)$[/tex][/tex] moves through space at [tex][tex]$3.0 \times 10^8 \, \text{m/s}$[/tex][/tex]. What is the frequency of the light?

A. [tex][tex]$7.41 \times 10^{-3} \, \text{Hz}$[/tex][/tex]
B. [tex][tex]$1.35 \times 10^2 \, \text{Hz}$[/tex][/tex]
C. [tex][tex]$6.67 \times 10^{14} \, \text{Hz}$[/tex][/tex]
D. [tex][tex]$1.50 \times 10^{-15} \, \text{Hz}$[/tex][/tex]



Answer :

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]