Determine the decay constant for (a) tritium, \(t_{1 / 2}=12.3 \mathrm{a}\); (b) lithium- \(8, t_{1 / 2}=0.84 \mathrm{~s}\); (c) nitrogen- \(13, t_{1 / 2}=10.0 \mathrm{~min}\).

Radioactive decay is a process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This natural phenomenon is spontaneous and changes the nucleus into a different atom. One common form of radiation emitted during radioactive decay is the alpha particle, which is essentially a helium nucleus; beta particles, which can be electrons or positrons; and gamma rays, which are high-energy photons.

When a nucleus undergoes radioactive decay, it transforms into a more stable isotope or a completely different element. This process continues until a stable or non-radioactive configuration is reached. The rate at which a radionuclide decays is characterized by the decay constant, which is unique for each radionuclide.

The half-life of a radionuclide is a critical concept in understanding radioactive decay. It is defined as the time required for half of the atoms in a radioactive sample to undergo decay. Half-life is inversely related to the decay constant; a radionuclide with a short half-life will decay more quickly and thus have a higher decay constant.

Half-life is an average measure; it does not mean that exactly half of the atoms will have decayed after one half-life period, but statistically, it provides an estimate of the time required for significant decay to occur. This concept is commonly used to date archaeological artifacts, understand medical isotopes for treatment, and manage nuclear waste disposal due to the predictive nature of the half-life in determining how long radioactivity persists.

A radionuclide is a type of atom that has an unstable nucleus and can undergo radioactive decay, leading to the emission of radiation. Radionuclides occur naturally, as with uranium or thorium isotopes, but they can also be artificially created in nuclear reactors or particle accelerators. These isotopes have various applications, including in medicine for diagnostics and treatment, in industry for inspection, and in science for research.

The properties of a radionuclide, such as its half-life and the type of radiation it emits, determine its usefulness for specific tasks. For example, isotopes with shorter half-lives are often used in medicine to minimize the amount of time the patient is exposed to radiation.

Exponential decay is a pattern of reduction over time that can be applied to various phenomena, with radioactive decay being a prime example. In this context, the quantity of radioactive material decreases exponentially over time, meaning the rate of decay is proportional to the amount of substance present at any given moment. The decay constant is key to this relationship, as it allows us to create mathematical models for how quickly a radioactive substance diminishes.

The exponential nature of decay means that there is no clear end point; the radioactive material never fully disappears but reduces to a point where it becomes negligible or undetectable. These models are essential tools for predicting the behavior of radioactive materials over time, ensuring proper handling and safety protocols, and even for applications like radiocarbon dating.