Potassium-42 is used to locate brain tumors. Its half-life is \(12.5\) hours. Starting with \(15.4 \mathrm{mg}\), what fraction will remain after 100 hours? If it was necessary to have at least \(1 \mu \mathrm{g}\) for a particular procedure, could you hold the original sample for 200 hours before using it?

Radioactive decay is a natural process in which an unstable atomic nucleus loses energy by emitting radiation. This process results in the transformation of the original nuclide into a different one. There are three primary types of radioactive decay: alpha, beta, and gamma.
Alpha decay involves the emission of an alpha particle, which is composed of two protons and two neutrons. Beta decay follows from the transformation of a neutron into a proton or a proton into a neutron, accompanied by the emission of an electron or a positron. Gamma decay, on the other hand, involves the release of gamma rays, which are high-energy photons.
A vital aspect of radioactive decay is that the rate of decay is exponential, which is described by the half-life concept.

Potassium-42 (K-42) is a radioactive isotope of potassium. It has a half-life of 12.5 hours and decays by beta emission. This makes it useful in medical applications, especially in locating brain tumors.
The significance of K-42 in medical procedures lies in its ability to emit beta particles, which can be detected by imaging technology to highlight abnormal tissues. When introduced into the body, K-42 accumulates in areas with high metabolism, such as tumors, making them easier to locate.
The short half-life of K-42 is beneficial as it allows for rapid imaging and reduces long-term radiation exposure to patients.

Nuclear chemistry involves the study of the changes that occur within atomic nuclei. It is a crucial field for understanding both beneficial and detrimental nuclear reactions.
Key concepts in nuclear chemistry include radioactive decay, nuclear fission (splitting of a heavy nucleus into two lighter nuclei), and nuclear fusion (combining two light nuclei to form a heavier nucleus). These processes release large amounts of energy, which can be harnessed for power generation or medical applications.
Nuclear chemistry also explains the behavior of radioisotopes, their decay patterns, and their applications in fields such as medicine, agriculture, and archaeology.

Half-life is the time required for half of a radioactive substance to decay. It is a constant property for each specific isotope. For K-42, the half-life is 12.5 hours.
The half-life formula helps in calculating the remaining quantity of a substance over time: \[ N(t) = N_0 \times \frac{1}{2}^\frac{t}{t_{1/2}} \]Where:

• \(N(t)\): Amount remaining after time \( t \)
• \(N_0\): Initial amount
• \(t\): Time elapsed
• \(t_{1/2}\): Half-life of the substance

The idea is that with each passing half-life, the remaining quantity is halved, creating an exponential decay pattern.

Radioisotopes are isotopes that exhibit radioactive decay. They have applications in numerous fields:

• Medicine: Used in diagnosis and treatment of diseases (e.g., K-42 for brain tumor detection)
• Agriculture: Employed to improve food preservation and pest control
• Archaeology: Utilized in dating ancient artifacts through carbon dating

Each radioisotope has a unique half-life and decay mode, making them suitable for specific applications. The study of radioisotopes helps scientists understand atomic behaviors and invent technologies for various real-world problems.