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Chapter 18: Problem 22

The ultraviolet spectrum can be divided into three regions based on wavelength: UV-A (315-400 nm), UV-B (280-315 \(\mathrm{nm})\), and UV-C \((100-280 \mathrm{nm})\). (a) Photons from which region have the highest energy and therefore are the most harmful to living tissue? (b) In the absence of ozone, which of these three regions, if any, are absorbed by the atmosphere? (c) When appropriate concentrations of ozone are present in the stratosphere, is all of the UV light absorbed before reaching the Earth's surface? If not, which region or regions are not filtered out?

Short Answer

Expert verified
(a) The UV-C region has the highest energy photons and is the most harmful to living tissue. (b) In the absence of ozone, the atmosphere absorbs the UV-C region. (c) When appropriate concentrations of ozone are present in the stratosphere, not all of the UV light is absorbed before reaching the Earth's surface. The UV-A region is not fully filtered out and can still reach the Earth's surface.

Step by step solution

01

Recall the photon energy formula

First, let's recall the formula for photon energy. The energy of a photon is given by the equation \(E = \dfrac{hc}{λ}\), where E is the energy, h is the Planck's constant (\(6.63 x 10^{-34} Js\)), c is the speed of light (\(3 x 10^8 m/s\)), and λ is the wavelength.
02

Identify the region with the highest energy photons

We are given the wavelength range for each UV region: - UV-A (315-400 nm) - UV-B (280-315 nm) - UV-C (100-280 nm) Since energy and wavelength are inversely proportional, the shorter the wavelength, the higher the energy of photons. Therefore, by comparing the wavelength ranges, we can conclude that the UV-C region has the shortest wavelengths and hence the highest energy photons, making it the most harmful to living tissue. Answer to part (a): The UV-C region has the highest energy photons and is the most harmful to living tissue.
03

Identify the regions absorbed by the atmosphere

Part (b) of the problem asks us to determine which of these three regions, if any, are absorbed by the atmosphere in the absence of ozone. The atmosphere is composed of different gases and particles, which primarily absorb wavelengths in the UV-C region. So, in the absence of ozone, the atmosphere absorbs UV-C region. Answer to part (b): In the absence of ozone, the atmosphere absorbs the UV-C region.
04

Determine the effect of ozone on the UV light absorption

Now, we need to analyze the effect of having appropriate concentrations of ozone in the stratosphere (part c). The ozone layer absorbs most of the harmful UV radiation, especially in the UV-C and UV-B regions since these have shorter wavelengths and higher energies. However, the ozone layer is not able to completely absorb all UV radiation, and some UV-A radiation can still reach the Earth's surface, as its wavelengths are relatively longer and have lower energy. Answer to part (c): When appropriate concentrations of ozone are present in the stratosphere, not all of the UV light is absorbed before reaching the Earth's surface. The UV-A region is not fully filtered out and can still reach the Earth's surface.

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