Barium-141 is a beta emitter. What is the half-life if a \(16.0-\mathrm{g}\) sample of the nuclide decays to \(0.500 \mathrm{~g}\) in 90 minutes?

Radioactive decay is a natural process by which an unstable atomic nucleus loses energy. It happens by emitting radiation. This decay can result in the atom changing into a different element or isotope.
There are several types of radioactive decay, including alpha, beta, and gamma decay. Each type involves releasing different particles or energy.
In this exercise, we focus on beta decay. Understanding radioactive decay is key to studying nuclear chemistry and half-life calculations.

A beta emitter is a type of radioactive substance that undergoes beta decay. During beta decay, a beta particle is emitted from the nucleus of an atom. There are two types of beta decay:

• Beta-minus (β⁻) decay: Involves the emission of an electron and an antineutrino from the nucleus.
• Beta-plus (β⁺) decay: Involves the emission of a positron and a neutrino.

In the case of Barium-141, which is a beta emitter, the nucleus emits a beta particle to become a more stable nuclide.

Nuclear chemistry is the field of chemistry that deals with radioactive elements and their properties. It includes the study of nuclear reactions, radioactive decay, and applications of radioactive materials.
Key aspects of nuclear chemistry involve understanding how changes in the nucleus affect the atom’s identity. This field combines principles of chemistry and physics to explain these changes.
Applications of nuclear chemistry are vast. They range from medical imaging and cancer treatment to dating archaeological finds and generating nuclear energy.
Nuclear chemists often work with concepts such as half-life, types of radiation, and nuclear reactions to understand and harness the power of these substances.

The half-life of a radioactive substance is the time needed for half the amount of the substance to decay.
To determine the half-life, you need to know two things: the initial and final amounts of the substance, and the total time elapsed.
In the example of Barium-141, we started with 16.0 grams and ended with 0.500 grams in 90 minutes. By using the formula: \text{ }\[ t_{1/2} = \frac{\text{total time}}{n} \]\text{ } we calculated that there were 5 half-lives in 90 minutes. Dividing 90 minutes by 5, we found the half-life is 18 minutes.
This calculation is crucial for many scientific and practical applications, such as dating rocks, treating diseases, and managing nuclear waste.