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What is the wavelength of an ultraviolet light with a frequency of 1.20 x 10¹⁵

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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.

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