Question

Electromagnetic Waves UV Radiation 

Some of us are all too familiar with the ill- effects of over-exposure to ultraviolet (UV) electromagnetic radiation, namely, sunburns (solar erythema). UV radiation can kill the skin cells immediately below the surface (part of the epidermal layer). Over the course of several minutes or several hours, as enough skin cells are killed or damaged, the body's natural immune response is triggered. The body responds to the damage with increased blood flow to the capillary bed of the dermis in order to bring in cells to repair the damage. The extra blood in the capillaries causes the redness — if you press on sunburned skin it will turn white and then return to red as the capillaries refill. Also, the damaged cells release chemicals that trigger the pain receptors in the nerve endings in the skin, making the skin sensitive and potentially painful. 

Ultraviolet light is typically divided into three categories. UV-A, which has been linked with malignant melanomas, has wavelengths between 400 nm and 320 nm. UV-B, which is the primary cause of sunburn and skin cancer, has wavelengths between 320 nm and 280 nm. Finally, the region known as UV-C extends from 280 nm to 100 nm, and is almost entirely absorbed by the Earth's atmosphere (and consequently it does not pose nearly as much of a health concern as the other two categories even though the energy of the UV-C rays is greater).

 1. What is the frequency range (in Hz) of each of these three categories? a. UV-A? b. UV-B? c. UV-C?

2. Our sun has a power output of roughly 3.87 1026 watts (W). This energy is transmitted essentially uniformly in all directions. By the time this radiation reaches the Earth, which has an average distance from the sun of 1.50 x 10²⁶ m, what is the intensity? (Recall that intensity is defined to be power per unit area). 

3. The energy from the sun is primarily in the infrared and visual wavelengths. The following table gives the distribution of the sun's energy over the given regions of the electromagnetic spectrum. 

With this in mind, what is the intensity contained just within the UV-B range? 

4. Thankfully, the Earth's atmosphere blocks a fair amount of this radiation as well. Only about 25% of the incoming UV-B radiation makes it to the surface of the earth. What is the intensity of the UV-B radiation at the surface of the earth? 

5. On a clear summer day with the sun overhead, how much energy is absorbed by the skin on your exposed forearms (assume a total surface area of 0.1 m) if you're out in the sun, unprotected, for three hours and all of the incident UV-B radiation is absorbed? (Most sunscreens are designed to absorb this radiation so that less penetrates into your skin and causes damage.)

Answer 1

1. a) 320 - 400 nm

b) 280 - 320 nm

c) 100 - 280nm

2. Intensity = Power/Surface area

Since the this power is uniformly transmitted in all directions, so by considering sphere we have

=> I = P/4$\pi$R² ; where R is the distance of the point where intensity has to be calculated

=> I = 3.87 x 10²⁶ W/4$\pi$(1.5 x 10¹¹m)²

=> I = 1368.7325 W/m²

3. SInce UV-B is 1.5% of sun's energy;

P_UV-B =1.5/100 x 3.87 x 10²⁶ W = 5.805 x 10²⁴ W

So the intensity I_UV-B = 5.805 x 10²⁴ W/4$\pi$(1.5 x 10¹¹m)² = 20.531 W/m²

4. Since 25% of the incoming radiation makes it to surface thus,

intensity I_UV-B,surface = 0.25 x 20.531 W/m² = 5.13275 W/m²

5. The power delivered to the skin of a person assuming a surface area of 0.1m²

P_S = I_UV-B,surface x surface area = 5.13275 W/m² x 0.1m² = 0.513275 W

So, in three hours the energy absorbed by the skin;

E = 0.513275 W x 3 x 60 x 60 s

=> E = 5543.37 J

Answer 2