Answer :
To find the frequency of orange light with a given wavelength, you can use the formula that relates the speed of light to frequency and wavelength. The formula is:
[tex]\[
\text{speed of light} = \text{frequency} \times \text{wavelength}
\][/tex]
Rearranging this formula to solve for frequency gives:
[tex]\[
\text{frequency} = \frac{\text{speed of light}}{\text{wavelength}}
\][/tex]
Given:
- The speed of light, [tex]\( c \)[/tex], is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
- The wavelength of the orange light is [tex]\( 6 \times 10^{-7} \)[/tex] meters.
Substitute these values into the formula:
[tex]\[
\text{frequency} = \frac{3 \times 10^8 \, \text{m/s}}{6 \times 10^{-7} \, \text{m}}
\][/tex]
Carrying out the division:
[tex]\[
\text{frequency} = 5 \times 10^{14} \, \text{Hz}
\][/tex]
Therefore, the frequency of orange light is [tex]\( 5 \times 10^{14} \, \text{Hz} \)[/tex].
From the given choices, [tex]\( 5 \times 10^{16} \)[/tex], [tex]\( 2 \times 10^{-15} \)[/tex], [tex]\( 5 \times 10^{-46} \)[/tex], and 180, the correct answer is not listed, so it seems there was a mistake in the options. The correct frequency based on calculations should be [tex]\( 5 \times 10^{14} \, \text{Hz} \)[/tex].
[tex]\[
\text{speed of light} = \text{frequency} \times \text{wavelength}
\][/tex]
Rearranging this formula to solve for frequency gives:
[tex]\[
\text{frequency} = \frac{\text{speed of light}}{\text{wavelength}}
\][/tex]
Given:
- The speed of light, [tex]\( c \)[/tex], is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
- The wavelength of the orange light is [tex]\( 6 \times 10^{-7} \)[/tex] meters.
Substitute these values into the formula:
[tex]\[
\text{frequency} = \frac{3 \times 10^8 \, \text{m/s}}{6 \times 10^{-7} \, \text{m}}
\][/tex]
Carrying out the division:
[tex]\[
\text{frequency} = 5 \times 10^{14} \, \text{Hz}
\][/tex]
Therefore, the frequency of orange light is [tex]\( 5 \times 10^{14} \, \text{Hz} \)[/tex].
From the given choices, [tex]\( 5 \times 10^{16} \)[/tex], [tex]\( 2 \times 10^{-15} \)[/tex], [tex]\( 5 \times 10^{-46} \)[/tex], and 180, the correct answer is not listed, so it seems there was a mistake in the options. The correct frequency based on calculations should be [tex]\( 5 \times 10^{14} \, \text{Hz} \)[/tex].