What percentage of cesium chloride made from cesium137 (beta emitter, \(t_{1 / 2}=30.1 \mathrm{y}\) ) remains after \(150 \mathrm{y}\) ? What chemical product forms?

Exponential decay is a fundamental concept in understanding the decrease of a quantity over time, especially in contexts like radioactive decay in nuclear chemistry. When an unstable nucleus undergoes radioactive decay, the number of original atoms decreases over time in a manner that can be modeled mathematically by an exponential function. In simple terms, this means that in each equal amount of time, a constant percentage of the remaining substance will decay, rather than a constant number of atoms.

For example, if a radioactive substance has a half-life of 30.1 years, this does not mean that exactly half of the atoms decay every 30.1 years. Rather, it signifies that the probability for each atom to decay within that period is such that, on average, half of the remaining atoms will have decayed by the end of one half-life. This concept is crucial in fields like medicine, archeology, and environmental science, where understanding the decay of substances over time can have significant implications.

Beta emission is one of the main types of radioactive decay. During beta emission, a beta particle, which is a high-speed electron or positron, is ejected from an atomic nucleus. This process occurs because the nucleus has an imbalance of neutrons and protons, and emitting a beta particle is a way for it to reach a more stable state.

In the case of cesium-137, a neutron in its nucleus turns into a proton while releasing an electron (a beta particle) and an antineutrino. This transformation results in a new element with an atomic number that is one higher than the original; cesium-137 becomes barium-137 after it undergoes beta decay. Understanding beta emission is not only key to grasping nuclear reactions but also to applications like radiation therapy and radiometric dating, where the properties of beta particles are utilized.

Nuclear chemistry is the sub-discipline of chemistry that deals with changes in the nucleus of elements and the energy that is consequently produced or used. This field encompasses the study of both stable and unstable isotopes, helping us to understand processes such as radioactive decay, nuclear fission, and nuclear fusion.

Radioactive isotopes, like cesium-137, are of particular interest as they can be used in various applications, ranging from medical treatments to energy generation in nuclear power plants. The rates at which these isotopes decay, characterized by their specific half-lives, are crucial for managing their use and understanding their impact on the environment. With each half-life, as radioactive isotopes decay, they form new elements, changing the chemical composition of a sample over time—propelling innovations in energy, medicine, and environmental science.