Radioactivity Help (page 4)
The nuclei of most familiar substances are stable. They retain their identities and remain unchanged indefinitely. However, some atomic nuclei change with time; they are unstable. As unstable atomic nuclei disintegrate, they emit high-energy photons and various subatomic particles. Radioactivity is a general term that refers to any of these types of radiation arising from the disintegration of unstable atoms.
Radioactivity, also called ionizing radiation because it can strip electrons from atoms, occurs in various forms. The most common are gamma rays (which we’ve already discussed), alpha (α) particles, beta (β) particles , and neutrinos . There are also some less common forms, such as high-speed protons and antiprotons, neutrons and antineutrons, and the nuclei of atoms heavier than helium.
Alpha particles are helium-4 (4He) nuclei traveling at high speeds. A4 He nucleus consists of two protons and two neutrons. An alpha particle has a positive electric charge because there are no negatively charged electrons surrounding it. As such, all alpha particles are ions. They have significant mass, so if they attain high enough speeds, they can acquire considerable kinetic energy. An alpha particle traveling at a sizable fraction of the speed of light (known as relativistic speed) attains an increased mass because of relativistic effects; this gives it additional kinetic energy. Most alpha particles can be blocked by modest barriers.
Beta particles are high-speed electrons or positrons. (Remember that a positron is the antimatter counterpart of the electron.) Any beta particle consisting of an electron, also called a negatron because it has a negative electric charge, is denoted β − , and any β particle consisting of a positron, which carries a positive charge, is denoted β + . All beta particles have nonzero rest mass (their mass when not moving at relativistic speed). Their kinetic energies are increased by relativistic effects if they move at near-light speeds.
Neutrinos are an entirely different sort of particle. They have no electric charge and no rest mass. They have tremendous penetrating power. The Earth is constantly being bombarded by neutrinos from space. These neutrinos have their origins in the cores of the Sun and distant stars. Most neutrinos pass through the entire planet unaffected. Sophisticated equipment is required to detect them. Neutrino detectors are placed far underground to block all other forms of radiation so that scientists can be sure the equipment is really detecting neutrinos and not stray particles of some other sort. The neutrino has a counterpart, known as the antineutrino .
In nature, radioactivity is produced by certain isotopes of elements with atomic numbers up to and including 92 (uranium). These are known as radioactive isotopes . An isotope of carbon, known as carbon-14 (14C), has eight neutrons. Atoms of 14 C are unstable; over time, they decay into carbon-12 (12C) atoms, which have six neutrons. Other examples of an unstable atoms include hydrogen-3 (3H), also known as tritium , which has a nucleus consisting of one proton and two neutrons; beryllium-7 (7Be), with a nucleus containing four protons and three neutrons; and 10Be, with a nucleus containing four protons and six neutrons.
In some instances, the most common isotope of a naturally occurring element also happens to be radioactive. Examples are radon, radium, and uranium. The barrage of cosmic particles from deep space can be considered a form of radioactivity, but these particles sometimes can create radioactive isotopes when they strike stable atoms in the Earth’s upper atmosphere.
Radioactivity is produced by a variety of human activities. The most well known in the early years of atomic research was the fission bomb . Its modern descendant is the vastly more powerful hydrogen fusion bomb . Such a weapon, when detonated, produces an immediate, intense burst of ionizing radiation. The high-speed subatomic particles produced in the initial blast, especially if the explosion occurs at or near the ground, cause large amounts of material to become radioactive. The resulting radioactive dust, called fallout , precipitates back to Earth over a period of time. Some fallout, especially from the largest nuclear bombs, can rise high into the troposphere and enter the jet streams, where it is carried around the globe.
Nuclear fission reactors contain radioactive elements. The heat from the decay of these elements is used to generate electrical power. Some byproducts of fission are radioactive, and because they cannot be reused to generate more power, they represent radioactive waste . Disposal of this waste is a problem because it takes many years, even centuries, to decay. If a fusion reactor is ever developed and put into use, it will be a vast improvement over the fission reactor because controlled hydrogen fusion produces no radioactive waste.
Radioactive isotopes can be produced by bombarding the atoms of certain elements with high-speed subatomic particles or energetic gamma rays. Charged particles are accelerated to relativistic speeds by particle accelerators , also known informally as atom smashers . A linear particle accelerator is a long, evacuated tube that employs a high voltage to accelerate particles such as protons, alpha particles, and electrons to speeds so great that they can alter or split certain atomic nuclei that they strike. A cyclotron is a large ring-shaped chamber that uses alternating magnetic fields to accelerate the particles to relativistic speeds.
Decay And Half-life
Radioactive substances gradually lose “potency” as time passes. Unstable nuclei degenerate one by one. Sometimes an unstable nucleus decays into a stable one in a single event. In other cases, an unstable nucleus changes into another unstable nucleus, which later degenerates into a stable one. Suppose that you have an extremely large number of radioactive nuclei, and you measure the length of time required for each one to degenerate and then average all the results. The average decay time is called the mean life and is symbolized by the lowercase Greek letter tau (τ).
Some radioactive materials give off more than one form of emission. For any given ionizing radiation form (alpha particles, beta particles, gamma rays, or other), there is a separate decay curve , or function of intensity versus time. A radioactive decay curve always has a characteristic shape: It starts out at a certain value and tapers down toward zero. Some decay curves decrease rapidly, and others decrease slowly, but the characteristic shape is always the same and can be defined in terms of a time span known as the half-life , symbolized t 1/2 .
Suppose that the intensity of radiation of a particular sort is measured at time t 0 . After a period of time t 1/2 has passed, the intensity of that form of radiation decreases to half the level it was at t 0 . After the half-life passes again (total elapsed time 2 t 1/2 ), the intensity goes down to one-quarter of its original value. After yet another half-life passes (total elapsed time 3 t 1/2 ), the intensity goes down to one-eighth its original value. In general, after n half-lives pass from the initial time t 0 (total elapsed time nt 1/2 ), the intensity goes down to 1/(2 n ), or 0.5 n , times its original value. If the original intensity is x 0 units and the final intensity is x f units, then
x f = 0.5 n x 0
The general form of a radioactive decay curve is shown in Fig. 18-9. The half-life t 1/2 can vary tremendously depending on the particular radioactive substance involved. Sometimes t 1/2 is a tiny fraction of 1 second; in other cases it is millions of years. For each type of radiation emitted by a material, there is a separate value of t 1/2 and therefore a separate decay curve.
Fig. 18-9 . General form of a radioactive decay curve.
Another way to define radioactive decay is in terms of a number called the decay constant , symbolized by the lowercase Greek letter lambda (λ). The decay constant is equal to the natural logarithm of 2 (approximately 0.69315) divided by the half-life in seconds. This is expressed as follows:
λ = 0.69315/ t 1/2
The symbol for the radioactive decay constant happens to be the same as the symbol for EM wavelength. Don’t confuse them; they are entirely different and independent quantities. Also, when determining the decay constant, be sure that t 1/2 is expressed in seconds. This will ensure that the decay constant is expressed in the proper units ( s −1 ). If you start with t 1/2 expressed in units other than seconds, you’ll get a decay constant that is the wrong number because it is expressed inappropriately.
The decay constant is the reciprocal of the mean life in seconds. Therefore, we can state these equations:
λ = 1/τ and τ = 1/λ
From these equations we can see that the mean life τ is related to the half-life t 1/2 as follows:
τ = t 1/2 /0.69315
= 1.4427 t 1/2
t 1/2 = 0.69315τ
Units And Effects
There are several different units employed to define overall radiation exposure. The unit of radiation in the International System of units is the becquerel (Bq), representing one nuclear transition per second (1 s −1 ). Exposure to radiation is measured according to the amount necessary to produce a coulomb of electric charge, in the form of ions, in a kilogram of pure dry air. The SI unit for this quantity is the coulomb per kilogram (C/kg). An older unit, known as the roentgen (R), is equivalent to 2.58 × 10 −4 C/kg.
When matter such as human tissue is exposed to radiation, the standard unit of dose equivalent is the sievert (Sv), equivalent to 1 joule per kilogram (1 J/kg). Sometimes you’ll hear about the rem (an acronym for roentgen equivalent man); 1 rem = 0.01 Sv.
All these units make it confusing to talk about radiation quantity. To make things worse, some of the older, technically obsolete units such as the roentgen and rem have stuck around, especially in laypeople’s conversations about radiation, whereas the standard units have been slow to gain acceptance. Have you read that “more than 100 roentgens of exposure to ionizing radiation within a few hours will make a person sick” or that “people are typically exposed to a few rems during a lifetime”? Statements like these were common in civil-defense documents in the 1960s after the Cuban missile crisis, when fears of worldwide nuclear war led to the installation of air-raid sirens and fallout shelters all over the United States.
When people are exposed to excessive amounts of radiation in a short time, physical symptoms such as nausea, skin burns, fatigue, and dehydration commonly occur. In extreme cases, internal ulceration and bleeding lead to death. When people get too much radiation gradually over a period of years, cancer rates increase, and genetic mutations also occur, giving rise to increased incidence of birth defects.
Radioactivity has numerous constructive applications in science, industry, and medicine. The most well known is the nuclear fission reactor, which was popular during the middle to late 1900s for generating electricity on a large scale. This type of power plant has fallen into disfavor because of the dangerous waste products it produces.
Radioactive isotopes are used in medicine to aid doctors in diagnosing illness, locating tumors inside the body, measuring rates of metabolism, and examining the structure of internal organs. Controlled doses of radiation are sometimes used in an attempt to destroy cancerous growths. In industry, radiation can be used to measure the dimensions of thin sheets of metal or plastic, to destroy bacteria and viruses that might contaminate food and other matter consumed or handled by people, and to x-ray airline baggage. Other applications include the irradiation of food, freight, and mail to protect the public against the danger of biological attack.
Geologists and biologists use radioactive dating to estimate the ages of fossil samples and archeological artifacts. The element most commonly used for this purpose is carbon. When a sample is created or a specimen is alive, there is believed to exist a certain proportion of 14C atoms among the total carbon atoms. These gradually decay into 12C atoms. By measuring the radiation intensity and determining the proportion of 14C in archeological samples, anthropologists can get an idea of how long ago the world’s great civilizations came into being, thrived, and declined. Climatologists used the technique to discover that the Earth has gone through cycles of generalized global warming and cooling.
Carbon dating has revealed that the dinosaurs suddenly and almost completely disappeared in a short span of time around 65 million years ago. By a process of elimination, it was determined that a large meteorite or comet splashed down in the Gulf of Mexico at that time. The Earth’s climate cooled off for years because of debris injected into the atmosphere following the impact that blocked much of the solar IR that normally reaches the surface. Further research has shown that there have been several major bolide impacts in the distant past, each of which has radically altered the evolutionary course of life on Earth. Based on this knowledge, most scientists agree that it is only a matter of time before another such event takes place. When—not if—it does, the consequences for humanity will be of biblical proportions.
Radioactivity Practice Problems
Suppose that the half-life of a certain radioactive substance is 100 days. You measure the radiation intensity and find it to be x 0 units. What will the intensity x 365 be after 365 days?
x 365 = 0.5 n x 0
where n is the number of half-lives elapsed. In this case, n = 365/100 = 3.65. Therefore:
x 365 = 0.5 3.65 x 0
To determine the value of 0.5 365 , use a calculator with an x y function. This yields the following result to three significant digits:
x 365 = 0.0797 x 0
What is the decay constant of the substance described in Problem 18-5?
λ = 0.69315/(8.64 × 10 6 )
= 8.02 × 10 −8 s −1
What is the mean life of the substance described in Problem 18-5? Express the answer in seconds and in days.
The mean life τ is the reciprocal of the decay constant. To obtain τ in seconds, divide the numbers in the preceding equation with the numerator and denominator interchanged:
τ= (8.64 × 10 6 )/0.69315
= 1.25 × 10 7
This is expressed in seconds. To express it in days, divide by 8.64 × 10 4 . This gives an answer of approximately 145 days.
Practice problems of these concepts can be found at: Forms of Radiation Practice Test
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