The speed of a light wave in a certain transparent material is 0.701 times its speed in vacuum, which is 3.00*108 m/s. When yellow light with a frequency of 5.23*1014 Hz passes through this material, what is its wavelength? in nanometers?

402 nm

Explanation:

First, we find the speed of light in this medium:

v = 0.701 * c

v = 0.701 * 3 * 10^8

v = 2.103 * 10^8 m/s

Speed of a wave is given as the product of wavelength and frequency:

v = λf

Where λ = wavelength

Wavelength, λ, becomes:

λ = v/f

The frequency of the light is 5.23 * 10^14 Hz, therefore, wavelength will be:

λ = (2.103 * 10^8) / (5.23 * 10^14)

λ = 4.02 * 10^ (-7) m = 402 nm

The wavelength of the light is 402 nm.