The relationship between the frequency (f) and the wavelength (λ) of light is given by the equation:
λ = c / f
where λ represents the wavelength, f is the frequency, and c is the speed of light in a vacuum (approximately 3.0 × 10^8 meters per second).
To convert the frequency from Hz to s^(-1), you need to multiply it by the appropriate unit conversion factor:
8.6 × 10¹³ Hz = 8.6 × 10¹³ s^(-1)
Now, we can substitute the values into the equation to find the wavelength:
λ = (3.0 × 10^8 m/s) / (8.6 × 10¹³ s^(-1))
Calculating this expression gives:
λ ≈ 3.49 × 10^(-7) meters
To convert this to nanometers, we multiply by 10^9 since there are 10^9 nanometers in a meter:
λ ≈ 3.49 × 10^(-7) meters × 10^9 nm/meter
λ ≈ 349 nm
Therefore, the wavelength of blue light with a frequency of 8.6 × 10¹³ Hz is approximately 349 nanometers.