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Ultraviolet radiation with a frequency of 5.32 x 10^15 Hz is used to disinfect water. What is the wavelength of this radiation?

A) 3.57 x 10^-7 meters
B) 1.87 x 10^-6 meters
C) 5.66 x 10^-8 meters
D) 1.88 x 10^-7 meters

1 Answer

4 votes

Final answer:

The wavelength of ultraviolet radiation with a frequency of 5.32 x 10^15 Hz is calculated using the formula λ = c/f and should be approximately 5.64 x 10^-8 meters. However, this result does not match any of the provided answer options, which suggests there may be an error in the question or the options.

Step-by-step explanation:

The question asks for the calculation of the wavelength of ultraviolet radiation used to disinfect water with a given frequency of 5.32 x 1015 Hz. To find the wavelength of electromagnetic radiation, we can use the equation c = λf, where c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s), λ is the wavelength, and f is the frequency. Plugging in the given frequency and rearranging the formula to solve for λ gives us: λ = c/f = (3.00 x 10^8 m/s) / (5.32 x 10^15 Hz) which calculates to a wavelength of approximately 5.64 x 10^-8 meters. This calculation result matches none of the provided choices A to D, so there may be an error in the question or options.

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