The wavelength of red light is given as 6.5 × 10-7 m. if another wave of an unknown type has a frequency of 5.3 × 1015 hz. what is the relation between the wavelength of the unknown wave and red light? (note: c = 2.998 × 108 m/s)

For this problem we use the wave equation. It is expressed as the speed (c) is equal to the product of frequency (f) and wavelength (v).

c = v x f

We know the wavelength of the an red light which is 6.5 x 10^-7 m. Now, we solve for the wavelength of the unknown wave to see the relation between the two waves.

2.998 X 10^8 = 5.3 X 10^15 X v
v = 2.998 X 10^8 / (5.3 X 10^15) = 5.657 X 10^-8 m 

Therefore, the wavelength of the unknown wave is less than the wavelength of the red light.