First, let's clearly state the question: We need to find the frequency of green light given its wavelength is approximately [tex]\( 500 \, \text{nm} \)[/tex] and knowing that [tex]\( 1 \, \text{nm} = 1 \cdot 10^{-9} \, \text{m} \)[/tex].
To find the frequency of light, we use the relationship between the speed of light ([tex]\( c \)[/tex]), the wavelength ([tex]\( \lambda \)[/tex]), and the frequency ([tex]\( f \)[/tex]) given by the formula:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
### Steps:
1. Convert the wavelength from nanometers to meters:
Given:
[tex]\[ \lambda = 500 \, \text{nm} \][/tex]
Convert nanometers to meters:
[tex]\[ \lambda = 500 \, \text{nm} \times 10^{-9} \, \text{m/nm} \][/tex]
[tex]\[ \lambda = 500 \times 10^{-9} \, \text{m} \][/tex]
[tex]\[ \lambda = 5.000 \times 10^{-7} \, \text{m} \][/tex]
2. Use the speed of light in a vacuum:
The speed of light ([tex]\( c \)[/tex]) is approximately:
[tex]\[ c = 3 \times 10^8 \, \text{m/s} \][/tex]
3. Calculate the frequency using the formula [tex]\( f = \frac{c}{\lambda} \)[/tex]:
Substitute the values we have:
[tex]\[ f = \frac{3 \times 10^8 \, \text{m/s}}{5.000 \times 10^{-7} \, \text{m}} \][/tex]
4. Perform the division:
[tex]\[ f = \frac{3 \times 10^8}{5.000 \times 10^{-7}} \][/tex]
[tex]\[ f = 0.6 \times 10^{15} \][/tex]
Or
[tex]\[ f = 6 \times 10^{14} \, \text{Hz} \][/tex]
So, the frequency of green light with a wavelength of [tex]\( 500 \, \text{nm} \)[/tex] is [tex]\( 6 \times 10^{14} \, \text{Hz} \)[/tex].
Therefore, the correct answer is:
[tex]\[ 6 \times 10^{14} \, \text{Hz} \][/tex]
