Chapter 5: Photons: Cell Phones, Sunlight and X-Rays

Electric power is, without question, one of the greatest inventions of the human species. Just think: You plug your gizmo into the wall socket, and out comes all the power you need, for as long as you need it. It’s cheap, too: An hour’s use of the electric company’s horse¹ costs less than a dime, and you don’t have to feed it or clean up afterwards. Electric power is one of the miracles we take for granted, and we notice it only when it is taken away, during those rare days of blackouts and violent storms. Electric power cools and heats your home, washes and dries your clothes and dishes, fires up your computer and television, and lights up your nights. It is, as a spokesman for the industry once said, women’s liberation, although he should have mentioned the birth control pill in the same breath.

Electric power isn’t entirely safe, of course. In the United States, about 1000 people die every year from accidental electrocution. That’s two or three in a million, roughly speaking, a small enough number that hardly anyone notices, except for the friends and kin of the deceased.

There are other hazards of living with electric power. Coal-fired power plants emit acids and particulates (dust), nuclear plants have radiation dangers, and hydroelectric plants despoil the landscape. These hazards are harder to quantify, although they are all surely real, if in some cases perhaps small. We are all guinea pigs in the progress of technology, although the good news is that, on balance, our life spans keep increasing, year after year.

One danger of electric power is almost surely not real – the presumed hazard of living under high voltage power lines, or, for that matter, sleeping under electric blankets. For a time it was widely believed that close proximity to electric power lines could cause a variety of health problems, including childhood leukemia and adult cancer. The belief originated in a statistical association. After much study, the association appeared to weaken, and has since been attributed to other causes. Wealthy neighborhoods can usually fight off having power lines placed locally; poor neighborhoods are not so successful. Poor people have more health problems.

More recently, an alarm was sounded over the use of cell phones. Maybe cell phones cause brain cancer. The alarm didn’t last very long. I think people found cell phones so convenient they were willing to ignore any unproved risk. The perceived risk in high-voltage power lines was economic: Unsightly power lines reduce property values. The perceived risk of cell phones seems limited to the annoyance of other people’s use, and the hazards of driving while dialing and talking.

To understand why most scientists think power lines and cell phones do not pose direct risks of health problems requires a little background in electromagnetic radiation and quantum mechanics. All radiation, from radio and television to visible light and x-rays, consists of particles of energy called photons. All photons move at the speed of light, but differ in the amount of energy each photon carries. Radio waves carry the least energy per photon, gamma rays and x-rays carry the most, and visible light is in between, blue light being more energetic, red light less so. Photons are absorbed by chemical matter in different ways depending on their energy: x-rays smash into matter and break chemical bonds, while radio waves have very mild effects that involve heating up whole molecules and making them move a little faster. An intense beam of radio waves cannot break chemical bonds, while even a weak beam of x-rays can. (So can the ultra-violet portion of sunlight.) This is why nuclear radiation, which consists of photons (and other particles) even more energetic than x-rays, is dangerous.

The “flux” of energy radiation can be stated in a couple of different ways. The common measure is watts per square meter of surface area (or watts per square centimeter), and a good standard is the sun’s radiation on the earth, about 1000 watts per square meter, or a tenth of a watt per square centimeter. This is about the same energy flux your skin would feel if you held your hand nine centimeters from a 100-watt light bulb. It’s warm, but safe. The other measure of flux is number of photons per square meter (or square centimeter) per second. For a standard of 0.1 watts per square centimeter, this varies enormously depending on whether each photon carries a lot of energy or a little. For radio and TV and cell phones, there are a lot more photons in 0.1 watt per square centimeter than in an equal beam of x-rays, but the x-rays would do serious damage to your hand, while a radio wave would probably do little more than heat your skin. It’s not the number of photons that matters most, but the energy per photon.

Living cells and organisms have repair mechanisms, and it seems likely that the human body can cope with low levels of nuclear radiation, just as it can cope with mild sunburn. For example, people who live at high altitudes, such as Colorado, are exposed to far higher levels of cosmic rays (a kind of super-energetic x-ray) than people who live at sea level, yet do not have higher cancer rates. It seems that there is a safe level of exposure to cosmic rays, below which no harm can be seen. On the other hand, people who spend a lot of time outdoors, exposed to the sun, have far higher rates of skin cancer. Photons of ultra-violet radiation from the sun have enough energy to break chemical bonds, cause real damage, and overwhelm the biological repair systems. When it comes to cell phones and electromagnetic radiation from power transmission lines and electric blankets, most scientists assume that it is extremely unlikely that the low energy photons involved can have any effect at all as long as the overall intensity of the radiation is below the level where strong heating can occur (as in a microwave oven). As long as the overall energy level is below that of sunlight it is difficult to see how such radiation can cause any harm. The photons that originate in a source like a cell phone are far too weak to break chemical bonds.

Could scientists be wrong about this? Yes. But I bet my life they aren't. So have tens of millions of fellow guinea pigs.

Here’s a much more detailed and technical way of talking about photons. The energy of a single photon is given by the formula E = h, where  = c/. (Energy equals Planck's constant times frequency; frequency equals the speed of light divided by wavelength). For example, from the second formula we can calculate that the wavelength of a cell phone operating on the 850-megahertz band ( = 850,000,000 hertz) is about a foot (35 centimeters, to be more exact), since the speed of light is 30,000,000,000 centimeters per second. From the first formula, the energy of a single photon from a cell phone antenna is 5.6 x 10^-25 joules. A watt is a joule per second, so a one-watt phone emits 1.8 x 10²⁴ photons per second. That's a lot of photons!

Consider, by contrast, the light from a candle, which emits about 0.0015 watts in the visible part of the spectrum. At a distance of a meter from the candle, the light intensity is about 1.2 x 10^-8 watts per square centimeter. At ten meters, 1.2 x 10^-10. At one hundred meters, 1.2 x 10^-12 watts per square centimeter. At this distance you can still see the candle, but your eye is receiving only three million photons per square centimeter per second. Since the diameter of your pupil is only about 6 millimeters (dark adapted), only about a million photons per second enter your eye, which has a focal length of about 1.7 centimeters, roughly f/3 in camera terms. The image of a candle one centimeter in diameter at a distance of 100 meters (10⁴ centimeters) has a diameter of only 1.7 x 10^-4 centimeters on your retina, or an area of 2.3 x 10^-8 square centimeters. This is less than the size of a single receptor cell! But your eye, by doing some clever movements, and some equally clever computing, can still see the candle, which is, in effect, a point source, like a star in the sky. The eye can see stars with a magnitude of 6 or less, corresponding to an intensity of about 10^-14 watts per square centimeter, or about 10,000 photons per second on your retina. And you could do even better with a flickering light source. As the figures below indicate, the eye can deal with an extraordinary range of intensities although, outside the range 400 to 700 nanometers, it has no sensitivity at all.

Visual acuity is another matter. The eye can only resolve two points that are farther apart than about a tenth of the diameter of the moon. This is equivalent to two objects a centimeter apart a thousand centimeters away. On your retina, these two points would be 1.7 x 10^-3 centimeters apart. A circular spot of this diameter would include about 30 receptor cells. This is why we cannot see the mountains of the moon without a telescope.

We have seen that the eye can deal with an extraordinary range of visible electromagnetic radiation, from 10^-14 to (perhaps) 10^-2 watts per square centimeter. What about x-rays?

X-rays are produced by accelerating electrons in a cathode ray tube (CRT), in much the same fashion as electrons are accelerated in the tube of a television set or a computer monitor. The voltages in an x-ray machine are a little higher, 60,000 volts versus 35,000 in a TV, but of course consumer CRTs use lead crystal glass to reduce x-ray emissions to a presumably safe level, while x-ray machines are designed to convert the energy of the electrons to x-ray photons. Due to losses in the conversion process, the average energy of an x-ray photon is about 30,000 “electron volts,” which corresponds to a wavelength of about 4 x 10^-9 centimeters.

X-ray wavelengths are extremely short, and are usually measured in Angstroms or nanometers or picometers. (One Angstrom is a tenth of a nanometer, or 10^-8 centimeters. A picometer is 10^-12 meters, or 10^-10 centimeters.) An x-ray photon with a wavelength of 40 picometers has an energy of 5 x 10^-15 joules. A flux of 0.1 watt per centimeter squared is equivalent to about 2 x 10¹³ photons per square centimeter per second. Actual x-ray exposures are far less intense, and the exposure lasts only a couple of seconds. What matters here is not the flux, but the total dose. A typical chest x-ray delivers a dose of 0.1 mSv (milliSieverts), where a Sievert² is defined as a joule of photon energy absorbed per kilogram of body mass. Assuming that your chest region weighs about ten kilograms, it absorbs about 0.001 joules of radiation during an x-ray. By way of comparison, a mere one-second exposure of your chest area (about 1000 square centimeters) to sunlight would deliver 100 joules. So a chest x-ray doesn’t sound like much radiation until you recall the difference in energy per photon. A dose of 10 Sieverts can kill you.

To understand what happens when the body is exposed to x-rays, consider that a ten Sievert dose to your chest area means that your body has absorbed 2 x 10¹⁶ photons, each one of which causes some damage to a chemical bond in your body. Ten kilograms of your body (which is mostly water) contains about 10²⁷ atoms. So only five atoms in 10¹⁰ are affected – five atoms in ten billion. Not many, surely, but enough to kill. Yet a dose one hundred thousand times smaller is presumably³ safe. Just why the disruption of only five atoms in ten billion can kill is not well understood, nor is it clear why smaller doses are safe. Biological systems have mechanisms for repairing cell damage or destroying damaged cells, and, presumably, as long as these mechanisms can keep up with the rate of damage, full and rapid restoration is likely. Once these mechanisms are overwhelmed, repair is no longer possible. A cell⁴ contains (very roughly) 1.5 x 10¹⁴ atoms, so a ten Sievert chest dose affects three cells in ten thousand. A dose of 0.1 mSv affects only three cells in a billion. That seems to be a level of damage your body can cope with.

What we have shown here is that the risk from radiation has little to do with overall intensity (as long as the intensity is insufficient to cook you). What matters is the way radiation and atoms interact. Weak photons from cell phones are probably harmless; stronger photons from visible light also cause little harm although the eye can detect amazingly low levels of energy. But when it comes to the highly energetic photons in x-rays and cosmic rays, very low doses of energy can destroy cells and kill, although it is likely that as long as only a small fraction of cells are killed, the body can cope.

Exercise #1. If cells were uniform spheres, packed together like oranges in a supermarket, they would occupy 74% of a given volume, with the rest taken up by intercellular fluid. Since there are approximately 675 million cells per cubic centimeter, such cells would have a diameter of 1.28 x 10^-3 centimeters. A: Verify this calculation. B: If cells were uniform cubes, with no intercellular fluid, show that the length of a side would be 1.14 x 10^-3 cm. C: If a uniform layer of cells had a thickness of just one cell, how many cells would there be in an area of 0.01 square centimeters? How does this compare with the density of cells in the central part of the retina? Why are these cells called rods?

Exercise #2. The average energy of an x-ray photon is about 30,000 electron-volts (eV), while the energy required to break a typical chemical bond is only about 3 eV. In principle, there is enough energy in an x-ray photon to break 10,000 bonds. It is generally believed that the damage caused when an x-ray photon interacts with a cell is extremely localized, confined to the immediate vicinity of the collision site, so that the interaction affects only one (or at most two) cells. This means that a 10 Sievert chest dose affects far more than five atoms in ten billion while still disrupting three cells in ten thousand. Compare the expected effects of a 10 Sievert dose of x-rays with the same dose of gamma radiation. Which dose damages more cells?

Exercise #3. In a photoelectric cell, a voltage and current are produced when the energy per photon of light on the cell is greater than a critical value. Weaker photons produce no effect, while more energetic photons produce one electron per photon at the critical voltage. (This is called the photoelectric effect; it was first explained by Einstein in 1905.) A modern solar panel consists of 36 silicon photoelectric cells wired in series, with a total open-circuit voltage of 21 volts, i.e., 0.58 volts per cell. What is the minimum energy per photon required to produce this voltage? What is the maximum effective wavelength? How goes this compare to the wavelength of yellow light, 5 x 10^-5 cm? How does this affect the efficiency of a silicon solar cell?

Exercise #4. The pixels in a digital camera are basically tiny silicon photoelectric cells. Each absorbed photon produces an electron, and the electrons are stored and later counted to produce an image. Since each absorbed photon produces only one electron, how is it possible to produce a colored image?

Exercise #5. The cells in your retina act in a way that is very similar to the pixels in a digital camera, except that photon absorption produces a reversible chemical change rather than an emitted electron. How is it possible for us to see colors?

© 2007 Peter O’Donnell Offenhartz