Question

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

Short answer

The frequency range of light that octyl methoxycinnamate and oxybenzone absorb is between \(0.938 \times 10^{15}\) Hz and \(1.071 \times 10^{15}\) Hz.

Step-by-step solution

Convert the wavelength range to meters

The wavelength range for UVB light is given in nanometers (nm). We need to convert this to meters (m) for our calculations. 1 nm = 1 x 10^(-9) m Wavelength range in meters: 280 nm to 320 nm = 280 x 10^(-9) m to 320 x 10^(-9) m

Set up the formula

The formula that relates speed of light, wavelength, and frequency is: c = λ × ν We will rearrange the formula to solve for frequency (ν): ν = c / λ

Calculate the frequency range

Now that we have the formula set up, we can substitute the values and calculate the frequency range. Remember, since we need to find the range, we need to do these calculations for both the lower and upper limits of the wavelength range. For lower wavelength limit (280 x 10^(-9) m): ν₁ = c / λ₁ ν₁ = (3.0 x 10^8 m/s) / (280 x 10^(-9) m) ν₁ = 1.071 × 10^(15) Hz For upper wavelength limit (320 x 10^(-9) m): ν₂ = c / λ₂ ν₂ = (3.0 x 10^8 m/s) / (320 x 10^(-9) m) ν₂ = 0.938 × 10^(15) Hz

Write the frequency range

Now that we have calculated the frequency range, we can write it down: Frequency range = 0.938 × 10^(15) Hz to 1.071 × 10^(15) Hz Octyl methoxycinnamate and oxybenzone absorb a frequency range of light between 0.938 × 10^(15) Hz and 1.071 × 10^(15) Hz.