Question

The letters following each Review Question refer to the corresponding Learning Objective from the Chapter Opener. What happens during radioactive decay and what does a half-life indicate? (E)

Short answer

During radioactive decay, unstable atomic nuclei lose energy by emitting radiation, transforming themselves to regain stability. The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay, and it is a characteristic property of each isotope. Half-lives help us understand how long it takes for a sample to become significantly less radioactive and have various applications in nuclear medicine, environmental monitoring, and dating geological samples.

Step-by-step solution

Introducing Radioactive Decay

Radioactive decay is a random process in which an unstable atomic nucleus loses energy by emitting radiation. This phenomenon occurs because certain atomic nuclei have an excess of energy, making them unstable. To regain stability, these nuclei spontaneously undergo a transformation, emitting energetic particles or electromagnetic radiation.

Types of Radioactive Decay

There are several types of radioactive decay, including alpha decay, beta decay, gamma decay, and others. In alpha decay, the nucleus emits an alpha particle, which consists of two protons and two neutrons. In beta decay, a neutron in the nucleus is transformed into a proton (or vice versa) and emits a beta particle (an electron or positron). Gamma decay involves the emission of gamma rays, which are high-energy photons, without changing the nucleus's composition. Each type of radioactive decay results in a different daughter nucleus with different properties.

Concept of Half-Life

Half-life is the time it takes for half of the radioactive nuclei in a sample to decay. In other words, after one half-life, 50% of the original nuclei have decayed, and 50% are still present. After two half-lives, 25% of the original nuclei remain, and so on. This concept is important because it helps us understand how long it takes for a radioactive sample to become significantly less radioactive, which has implications in several areas, such as nuclear medicine, environmental monitoring, and dating geological samples.

Properties of Half-Life

The half-life of a radioactive isotope is a characteristic property, i.e., it does not depend on the amount or physical state of the material. Different isotopes have different half-lives, ranging from fractions of a second to millions of years. Since radioactive decay is a random process, the half-life represents the average time it takes for half of the radioactive nuclei to decay. However, for a large enough number of nuclei, the half-life can be used to make statistical predictions about the decay of a sample. In conclusion, radioactive decay is a process in which unstable atomic nuclei transform themselves to regain stability, emitting particles or electromagnetic radiation in the process. The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay, and it is a characteristic property of each isotope. Understanding radioactive decay and half-lives is essential for several practical applications, such as nuclear medicine, environmental monitoring, and dating geological samples.

Key concepts

Understanding Half-Life

The concept of half-life is central to the study of radioactive decay, as it determines the rate at which a radioactive material loses its radioactivity. It's an averaging measure telling us how long it takes for half of a given number of unstable atomic nuclei to undergo radioactive decay.

Imagine you have a sample containing 100 unstable atoms. If the half-life of these atoms is one year, after one year, you'd expect to have about 50 atoms left undecayed. After another year (two half-lives), you would have about 25 atoms remaining. Importantly, it's worth noting that even after several half-lives, some radioactive atoms will always remain; they just become less and less numerous over time.

This concept has practical applications, such as determining the dosage of radioactive isotopes in medical treatments, the safe time to wait after a nuclear spill, and the dating of archaeological findings through carbon dating, which relies on the half-life of Carbon-14.

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle – essentially a helium nucleus with 2 protons and 2 neutrons.

For example, take Uranium-238. Over time, it sheds an alpha particle, transforming into Thorium-234. This process releases energy and is one way an unstable atom can achieve a more stable configuration. Alpha particles, being relatively heavy and positively charged, can't travel far in air and can be stopped by a sheet of paper or even the outer layer of human skin, which minimizes their ability to damage living tissue when encountered outside the body. However, if alpha-emitting substances are ingested or inhaled, they can harm internal biological tissues.

Beta Decay

Beta decay is another decay mode wherein a radioactive atom turns one of its neutrons into a proton, or vice versa, leading to the release of an electron (beta minus decay) or a positron (beta plus decay).

In beta minus decay, an electron is ejected from the nucleus, accompanied by an antineutrino, shifting the nuclear charge positively by one unit. Conversely, beta plus decay emits a positron and a neutrino, with the nucleus losing a positive charge. As a result, the parent atom transmutes into a different element with a closer balance of protons to neutrons, moving towards stability. Beta particles are more penetrating than alpha particles but can be stopped by a few centimeters of plastic or a thin sheet of metal.

Gamma Decay

Gamma decay involves an unstable nucleus shedding excess energy by emitting a photon, known as a gamma ray. This emission can follow alpha or beta decay if those processes leave the daughter nucleus in an excited state.

Unlike alpha and beta decay, gamma decay does not alter the number of protons or neutrons in the nucleus. Instead, it brings an excited nucleus down to its ground state. Gamma rays are highly energetic and can penetrate most materials, including human tissue. As such, they are often used in medical imaging techniques like PET scans but require heavy shielding, such as lead or thick concrete, to protect against their potential harm.