Question

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

Short answer

Answer

Frequency range of ultraviolet light is ${\text{9.4×10}}^{\text{14}}{\text{s}}^{\text{- 1}}{\text{to1.1×10}}^{\text{15}}{\text{s}}^{\text{- 1}}$.

Step-by-step solution

Frequency and energy of a wave.

The formula to calculate frequency is

$\mathit{\lambda }\mathbf{.}\mathit{v}\mathbf{=}\mathit{c}$

Where,

$\mathrm{\lambda }$denotes wavelength.

v denotes frequency.

c denotes speed of light.

As per Planck's hypothesis, the energy associated with photon is given as follow:

E=h.v

Where,

v denotes frequency.

h denotes Planck's constant.

Avogadro's number is 6.022localid="1664342896884" $\times$10²³ photon/mol.

Frequency range of ultraviolet light.

Wavelength of UV radiation is in the range 280 nm to 320 nm.

The conversion factor to convert nm to is as follows:

$1\text{nm}={10}^{-9}\text{m}$

Thus, 280 nm is converted to as follows:

$$\begin{gathered} \text{Wavelength = (280nm)}\left(\frac{{\text{10}}^{\text{- 9}}\text{m}}{\text{1nm}}\right) \\ {\text{= 2.8×10}}^{\text{- 7}}\text{m} \end{gathered}$$

Similarly, is converted to as follows:

$$\begin{gathered} \text{Wavelength = (320nm)}\left(\frac{{\text{10}}^{\text{- 9}}\text{m}}{\text{1nm}}\right) \\ {\text{= 3.2×10}}^{\text{- 7}}\text{m} \end{gathered}$$

The formula to calculate frequency is as follows:

$v=\frac{c}{\lambda }$

When ${\text{λis2.8 10}}^{\text{- 7}}\text{m}$.

Value of c is${\text{3 10}}^{\text{8}}\text{m/s}$.

Substitute the value in above equation.

$$\begin{gathered} V=\frac{c}{\lambda } \\ \text{=}\frac{\text{3}{\text{1×0}}^{\text{8}}\text{m/s}}{\text{2.8}{\text{1×0}}^{\text{- 7}}\text{m}} \\ {\text{= 1.0714×10}}^{\text{15}}{\text{s}}^{-1} \end{gathered}$$

When is $\text{λis3.2}{\text{1×0}}^{\text{- 7}}\text{m}$.

Substitute the value in above equation.

$$\begin{gathered} V=\frac{c}{\lambda } \\ \text{=}\frac{{\text{31×0}}^{\text{8}}\text{m/s}}{{\text{3.2×0}}^{\text{- 7}}\text{m}} \\ {\text{= 0.9375×10}}^{\text{15}}{\text{s}}^{\text{- 1}} \\ \text{= 9.4}{\text{1×0}}^{\text{14}}{\text{s}}^{\text{- 1}} \end{gathered}$$

Thus, frequency range of ultraviolet light is ${\text{9.4 10}}^{\text{14}}{\text{s}}^{\text{- 1}}\text{to1.1}{\text{1×0}}^{\text{15}}{\text{s}}^{\text{- 1}}$.