Final answer:
The wavelength of radiation with a frequency of 5 x 10¹⁴ per second is 0.5996 meters. This is found using the equation c = λ * f, where c is the speed of light (2.998 x 10⁸ m/s) and λ is the wavelength in meters.
Step-by-step explanation:
To calculate the wavelength of radiation with a frequency of 5 x 10¹⁴ per second, we will use the relationship between wavelength (λ), frequency (f), and the speed of light (c). According to the wave equation c = λ * f. The speed of light (c) is a constant 2.998 x 10⁸ meters per second.
Using the given frequency (f) of 5 x 10¹⁴ Hz, we can rearrange the equation to solve for wavelength (λ): λ = c / f.
So, λ = (2.998 x 10⁸ m/s) / (5 x 10¹⁴ Hz) = 0.5996 meters. Therefore, the wavelength of the radiation is 0.5996 meters, which can also be expressed as 599.6 nanometers (nm), since 1 meter is equivalent to 1 x 10⁹ nm.