What is radioactivity and why does it occur?

Radioactivity is the spontaneous transformation of an unstable nuclide, resulting in radiation emission. This random process occurs because all nuclei in a sample have the same probability of decaying, regardless of sample size or conditions. The decay is an intrinsic property of unstable atoms seeking greater stability.

How is radioactive decay activity measured and what are its units?

Activity measures the number of disintegrations per unit time and is directly proportional to the number of radioactive nuclei present. The SI unit is the becquerel, equal to one disintegration per second. The curie, still used for large-scale applications, equals 37 billion becquerels.

What is half-life and how does it relate to decay constant?

Half-life is the average time required for a sample's activity to decrease to half its original value. It is inversely proportional to the decay constant, an intrinsic property unique to each radionuclide. Half-lives vary dramatically: radon-220 has a one-minute half-life, while thorium-232 has a 14-billion-year half-life.

How does carbon-14 dating determine the age of archaeological specimens?

Living organisms maintain a carbon-14 to carbon-12 ratio matching the atmosphere through continuous carbon replenishment. After death, carbon-14 decays by emitting beta particles while carbon-12 remains stable. By measuring the current ratio and comparing it to the atmospheric ratio, scientists calculate how many half-lives have elapsed, determining the specimen's age.

Why is carbon-14 dating limited to approximately 50,000 years?

Carbon-14 dating accuracy depends on detecting measurable carbon-14 levels in samples. With a half-life of 5,730 years, after about nine half-lives (approximately 50,000 years), carbon-14 levels become too low for reliable detection using standard methods. Beyond this timeframe, the remaining radioactive carbon is insufficient for precise age determination.

How do scientists use uranium-238 to date ancient rocks?

Uranium-238 decays into lead-206 over 4.5 billion years (its half-life). By measuring the uranium-238 to lead-206 ratio in rocks that contained no lead when formed, scientists can calculate the rock's age. This method works for much older geological samples than carbon-14 dating because of uranium-238's extremely long half-life.

What does the decay constant represent in radioactive decay calculations?

The decay constant is the average probability of decay per nucleus per unit time. It determines how quickly a radionuclide decays and is inversely proportional to half-life. Different radionuclides have different decay constants, reflecting their unique nuclear stability and decay rates.

19.5

Radioactive Decay and Radiometric Dating

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Radioactivity is the spontaneous transformation of an unstable nuclide, which results in the emission of radiation. This is a random process, so all the nuclei in the sample have the same probability of decaying.

The number of disintegrations per unit time is called the activity, A, which is directly proportional to N, the number of radioactive nuclei. Lambda, the decay constant, is the average probability of decay per nucleus per unit time.

Activity is measured with radiation detectors and has the becquerel, which is one disintegration per second, as its SI unit. The curie, which is 37 billion becquerels, is still used for large-scale applications.

Different radionuclides have different decay rates. As the activity is proportional to the number of radioactive atoms, it decreases with time as the amount of unstable nuclei in the sample decreases.

The change in activity over time is calculated with an exponential equation, where A is the activity at time t, A₀ is the initial activity, lambda is the decay constant, and t is the time elapsed since the activity was A₀.

The half-life of a radionuclide, t_1/2, is the average time required for the activity of a sample to fall to half of that value. Thus, the equation can be rearranged to calculate the half-life from the decay constant, to which it is inversely proportional.

The half-life is an intrinsic property of a radionuclide, and it varies widely from nuclide to nuclide: radon-220 has a half-life of one minute, whereas thorium-232 has a half-life of 14 billion years.

The fixed half-lives of radionuclides are relevant for techniques like radiometric dating, which estimates the age of objects from the quantity of naturally occurring radionuclides.

The ratio of unstable carbon-14 to stable carbon-12 in living plants and animals matches that of the atmosphere.

The ratio is maintained by replenishment of carbon from the air and food. After death, the carbon-14 to carbon-12 ratio begins decreasing as the radioactive carbon-14 decays by emitting beta particles.

If a specimen has 25% as much carbon-14 as it did when it was alive, then two half-lives must have elapsed. The object must be 11,460 years old.

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Radioactivity is a spontaneous disintegration of an unstable nuclide and is a random process, as all the nuclei in the sample do not decay simultaneou…