The relationship between the wavelength and the frequency is given by this equation:
λ = c/f
Where λ is the wavelength, f is the frequency and c is the speed of light.
We are given the frequency. f = 7.66 *10¹⁴ 1/s
C is a constant. c = 3 * 10⁸ m/s
λ is our unknown. So we can calculate the wavelength using the formula that we wrote before.
λ = c/f
λ = (3 * 10⁸ m/s) / (7.66 *10¹⁴ 1/s)
λ = 3.92 *10⁻⁷ m
The wavelength of light with the frequency given is 3.92 *10⁻⁷ m, but we are asked for the answer in nm. We have to convert the answer. There are 1*10⁹ nm in 1 m, then the conversion is:
1 m = 1 * 10⁹ nm
λ = 3.92 *10⁻⁷ m * 1 * 10⁹ nm/(1 m)
λ = 392 nm
Answer: The wavelength is 392 nm.