Final answer:
The wavelength of an ultraviolet light with a frequency of 1.20 x 10¹⁵ Hz is 250 nm. This calculation involves the use of the speed of light, and it also provides insight into the smallest detail observable with a microscope using this wavelength.
Step-by-step explanation:
The question asks to determine the wavelength of an ultraviolet light with a frequency of 1.20 x 10¹⁵ Hz. We can use the formula that relates the speed of light (λν = c), where λ is wavelength, ν is frequency, and c is the speed of light in a vacuum (approximately 3.0 x 10⁸ m/s). The formula to calculate wavelength is λ = c / ν.
Using the frequency value provided, the calculation for wavelength is:
λ = 3.0 x 10⁸ m/s / (1.20 x 10¹⁵ Hz)
λ = 2.5 x 10⁻⁷ meters
To convert from meters to nanometers (nm), since 1 m = 10⁹ nm, we have:
λ = 2.5 x 10⁻⁷ m x 10⁹ nm/m
λ = 250 nm
Therefore, the wavelength of the ultraviolet light is 250 nm. The smallest detail observable with a microscope using this wavelength would correspond to the wavelength, which is 250 nm, as resolution is typically limited to the wavelength of light used.