On average sunlight shines on the surface of Earth with an...

On average sunlight shines on the surface of Earth with an intensity of 910 Watts/m. . Some of this energy is in the form of ultraviolet (UV) radiation. The compounds in chemical sunscreens absorb ultraviolet rays and release the energy as lower-energy infrared (IR) rays, thereby preventing the skin-damaging UV rays from reaching the skin. You may have noticed references to UV-A $(320-400 \mathrm{nm})$ and $\mathrm{UV}-\mathrm{B}(280-320 \mathrm{nm})$ protection in sunscreen packaging and advertisements. Figure at lists the chemical formula and molar mass of two compounds, 2-ethylhexyl $p$ -methoxycinnamate $(2-\mathrm{EHMC}),$ a UV-B sunscreen, and terephthalylidenedicamphor sulfonic acid (TDSA), a UV-A sunscreen.

Key Concepts

UV-A and UV-B

UV-A and UV-B are two classifications of ultraviolet radiation characterized by different wavelength ranges. UV-A has a longer wavelength and penetrates deeper into the skin, while UV-B has a shorter wavelength and is primarily associated with causing sunburn. Awareness of these distinctions is important in the design and labeling of sunscreen products.

Energy Conversion in Sunscreens

Many chemical sunscreens work by absorbing high-energy ultraviolet rays and converting them into lower-energy forms, such as infrared radiation. This conversion process helps in reducing the amount of harmful UV energy reaching the skin, thereby preventing damage.

Ultraviolet (UV) Radiation

Ultraviolet radiation is a type of electromagnetic radiation with wavelengths shorter than visible light but longer than X-rays. It is divided into different bands based on wavelength ranges, and although it can be beneficial in small doses, excessive exposure can lead to skin damage and other health issues.

Solar Irradiance

Solar irradiance refers to the power per unit area received from the sun in the form of electromagnetic radiation. It is measured in watts per square meter and represents the energy available at the Earth's surface, which is crucial for processes like photosynthesis and the generation of solar power.

Transcript

00:01 So this question gives a bunch of information as well as a figure and a table, and then wants us to answer a series of questions based on that information.

00:10 And so question a is calculate the energy absorbed by tdsa at its maximum absorption for one photon of uv radiation.

00:19 And so energy of a photon is hc over lambda.

00:24 So 6 .626 times 10 to the negative 34th joules seconds times the speed of light 3 .00 times 10 to the 8th meters per second and then divided by the max absorption wavelength for tdsa which based on the figure is 335 nanometers so we'll multiply that by 10 to the minus ninth to get that into meters and so therefore the energy of a photon of tdsa is 5 0 .934 times 10 to the negative 19th joules.

01:02 Now letter b is the same question, calculate the energy absorbed, except in this time it's 2 ehmc at its maximum absorption for one photon of uv radiation.

01:13 So we use the same formula.

01:15 E photon equals hc over lambda.

01:18 So our h is 6 .626 times 10 to the negative 34th joules seconds times speed of light.

01:28 3 .00 times 10 to the 8th meters per second, and then divided by the max absorption wavelength of 2ehmc, which is 310, and then times 10 to the negative 9th to convert it from nanometers to meters to meters.

01:43 And that gives us an energy of a photon for 2ehmc to be 6 .412 times 10 to the negative 19th joules.

01:53 Now letter c asks which of these two compounds, or which absorbs more energy, 2ehmc or tdsa at their maximum wavelengths.

02:05 And so the answer to that is 2ehmc.

02:11 And we can look at our answers for a and b and determine that 2ehmc absorbs more energy.

02:19 Now for letter d, the question says, why are these two compounds commonly included in sunscreen products, and that's because one absorbs primarily uva light and one absorbs primarily uvb light.

02:32 So with both of them together, you're absorbing uva and uvb.

02:38 Now, letter e says a person does not apply sunscreen and has 0 .42 meters squared of skin exposed for one hour.

02:47 Calculate the total energy absorbed by the skin.

02:50 And so the way that we first do this is find the energy of a single photon, hc over lambda.

02:58 So h is 6 .626 times 10 to the negative 34th joules seconds times the speed of light, 3 .00 times 10 to the 8th meters per second.

03:10 And for this, it tells us to assume a wavelength of 330 nanometers.

03:16 So again, we'll multiply that by 10 to the minus ninth to convert to meters.

03:21 And that gives us an e -photon of 6 .026 times 10 .5 .5 .5 .5 .5.

03:25 And that gives us an e -photon of 6 .0236 times to the negative 19th, and that is joules per photon.

03:32 And so now that we have that, we can determine the remainder of the problem.

03:36 So we'll start with that 6 .0236 times 10 to the negative 19th joules per photon.

03:45 We're told to assume a rate of photons of 3 .066 times 10 to the 21st photons per meters squared second.

03:57 And we're told that half of these are reflected by the skin.

04:03 We have 0 .42 meters squared of skin exposed, and there are 3 ,600 seconds in one hour...

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