Final answer:
The frequency of light with a wavelength of 5.89 × 10⁻⁷ m is calculated to be 5.09 × 10¹⁴ Hz using the equation λ × v = c, where c is the speed of light.
Step-by-step explanation:
To find the frequency of light having a wavelength of 5.89 × 10⁻⁷m, we use the equation that relates the speed of light (c), frequency (v), and wavelength (λ):
c = λ × v
Where:
- Speed of light (c) is approximately 3.00 × 10⁸ m/s
- Wavelength (λ) is 5.89 × 10⁻⁷ m
First, we'll rearrange the equation to solve for frequency:
v = c / λ
Substituting the values we have:
v = (3.00 × 10⁸ m/s) / (5.89 × 10⁻⁷ m)
Calculating the frequency gives us:
v ≈ 5.09 × 10¹⁴Hz
This means that the frequency of light with a wavelength of 5.89 × 10⁻⁷ m is 5.09 × 10¹⁴ Hz to the hundredths place.