Question

The ultraviolet spectrum can be divided into three regions based on wavelength: UV-A \((315-400 \mathrm{nm}), \mathrm{UV}-\mathrm{B}(280-315\) \(\mathrm{nm} ),\) and \(\mathrm{UV}-\mathrm{C}(100-280 \mathrm{nm}) .\) (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

Using the photon energy formula \(E = \frac{hc}{\lambda}\), we find the energy ranges for the three UV regions: UV-A (315-400 nm), UV-B (280-315 nm), and UV-C (100-280 nm). The highest energy photons are in the UV-C region, making them the most harmful to living tissue. Without ozone, the atmosphere absorbs most of the UV-C radiation, leaving UV-A and UV-B to reach the Earth's surface. When appropriate ozone concentrations are present, all of the UV-C radiation and a significant portion of the UV-B radiation are absorbed. However, not all UV light is filtered out, with most UV-A radiation and some UV-B radiation still reaching the Earth's surface.

Step-by-step solution

Calculate the photon energy in each UV region

First, we need to find the energy of the photons in each region. We'll use the energy formula E = h(c/λ). Here, h = 6.63 x 10^-34 Js (Planck's constant), and c = 3.00 x 10^8 m/s (speed of light). We will calculate the energy range for each wavelength range given: UV-A: λ = 315-400 nm UV-B: λ = 280-315 nm UV-C: λ = 100-280 nm Remember to convert the wavelength from nanometers to meters before doing the calculation (1 nm = 1 x 10^-9 m).

Determine the highest energy UV region

After calculating the energy range for each UV region, we will compare and identify the region with the highest energy photons. Photons with higher energy are more harmful to living tissues.

Determine the effect of the atmosphere and ozone on UV regions

We will analyze the effect of atmospheric absorption on each UV region in the absence of ozone. This information will help us determine which UV regions are absorbed by the atmosphere when ozone is not present. Next, we will examine the role of ozone in absorbing UV light and identify which UV regions are entirely filtered out when appropriate concentrations of ozone are present in the stratosphere. This will help us determine which UV regions are not filtered out and can reach the Earth's surface.

Key concepts

Photon Energy Calculation

Understanding the energy of photons within the ultraviolet spectrum is pivotal for a range of scientific applications, from studying environmental impacts to designing protective materials. The energy of a photon is inversely proportional to its wavelength, following the formula \( E = h \frac{c}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) represents the photon's wavelength.

For UV-A (\( 315-400 \, \text{nm} \)), UV-B (\( 280-315 \, \text{nm} \) ), and UV-C (\( 100-280 \, \text{nm} \)), one can determine that UV-C photons have the highest energy due to their shortest wavelengths. It's this higher energy that contributes to the potential harm UV-C can inflict on living tissues, making it the most dangerous among the UV spectrum.

UV Radiation Effects

The ultraviolet radiation that reaches the Earth has profound effects on both the environment and living organisms. UV radiation can lead to skin damage, including sunburn, premature aging, and an increased risk of skin cancer in humans. Additionally, it can also affect other living organisms, disrupting growth and reproductive patterns.

UV radiation's impact extends to materials like plastics and paints, causing them to degrade over time. Therefore, it is crucial for scientific and medical research to understand the penetrative abilities of different UV regions to protect against these detrimental effects effectively.

Ozone Layer Absorption

The ozone layer serves as a protective shield, absorbing a significant portion of the UV radiation, particularly in the UV-C and UV-B regions. The absorption of UV-C is nearly complete, thanks to the ozone molecules, which strongly absorb photons in this region, preventing them from reaching the Earth's surface.

In the absence of the ozone layer, Earth would be exposed to much higher levels of harmful UV radiation. Surprisingly, a part of UV-B does make it through the ozone layer, although in a considerably attenuated form. UV-A is absorbed the least and thus represents the majority of UV radiation that reaches the ground, leading to the relatively higher safety measures needed against this particular range during outdoor activities.