Octyl methoxycinnamate and oxybenzone are common ingredients in sunscreen applications. These compounds work by absorbing ultraviolet (UV) B light (wavelength 280–320 nm), the UV light most associated with sunburn symptoms. What frequency range of light do these compounds absorb?

To make our calculations easier, we'll convert the given wavelength range of 280 nm to 320 nm into meters. Since 1 nm = 10^-9 m, we multiply each value by 10^-9 to convert them to meters. Wavelength range: 280 nm - 320 nm \(280\ nm\times10^{-9}\frac{m}{nm}=2.8\times10^{-7} m\) \(320\ nm\times10^{-9}\frac{m}{nm}=3.2\times10^{-7} m\) The converted wavelength range is now \(2.8\times10^{-7}\) m to \(3.2\times10^{-7}\) m.

Now, we will use the speed of light formula to determine the frequency range related to the given wavelength range. The formula for the speed of light is: \(c = \lambda \times f\) Where c is the speed of light (3 x 10^8 m/s), λ is the wavelength, and f is the frequency. To find the frequency range, we will rearrange the formula to solve for the frequency (f): \(f = \frac{c}{\lambda}\) We will calculate the frequencies corresponding to 280 nm and 320 nm wavelengths to find the range. For the lower end of the wavelength range: \(f_1 = \frac{3\times10^8\ m/s}{2.8\times10^{-7}\ m} \approx 1.071\times10^{15}\ Hz\) For the upper end of the wavelength range: \(f_2 = \frac{3\times10^8\ m/s}{3.2\times10^{-7}\ m} \approx 9.375\times10^{14}\ Hz\)

Based on our calculations, the compounds in sunscreen absorb light with frequencies in the range of: Approximately \(9.375\times10^{14}\ Hz\) to \(1.071\times10^{15}\ Hz\) This is the frequency range of the ultraviolet (UV) B light that octyl methoxycinnamate and oxybenzone absorb to protect the skin from sunburn symptoms.