High School

What is the wavelength (in nanometers) of ultraviolet radiation with a frequency of [tex]3.07 \times 10^{15} \, \text{s}^{-1}[/tex]?

A. 97.7 nm
B. [tex]9.77 \times 10^{-8}[/tex] nm
C. [tex]1.02 \times 10^{7}[/tex] nm
D. [tex]1.02 \times 10^{-2}[/tex] nm

Answer :

Final answer:

The wavelength of ultraviolet radiation with a frequency of 3.07×10^15 s^−1 is approximately 97.7 nm. Thus, option (a) is the correct answer.

Explanation:

To find the wavelength of ultraviolet radiation with a frequency of 3.07×10^15 s^−1, we can use the formula for the speed of light, which states that the speed of light (c) is equal to the product of wavelength (λ) and frequency (v), expressed as c = v * λ. Given that the speed of light is about 3.0 x 10^8 m/s or 3.0 x 10^17 nm/s, we substitute the given values into the formula to solve for wavelength:

λ = c / v
λ = (3.0 x 10^17 nm/s) / (3.07 x 10^15 s^-1)
λ ≈ 97.7 nm

Therefore, the wavelength of the ultraviolet radiation is approximately 97.7 nm, which corresponds to option a.

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