Question

If \(5 \mathrm{~g}\) of a radioactive substance has \(\mathrm{t}_{1 / \mathrm{s}}=14 \mathrm{hr}, 10 \mathrm{~g}\) of the same substance will have a \(\mathrm{t}_{1,}\) equal to (a) 14 hours (b) 28 hours (c) 50 hours (d) 70 hours

Short answer

The half-life is 14 hours (option a).

Step-by-step solution

Understanding Half-Life

The half-life of a radioactive substance is the time required for half of the substance to decay. Here, the half-life given for the substance is 14 hours. This property is independent of the initial quantity of the substance.

Analyzing the Problem

We are given that 5 g of the substance has a half-life (t_{1 / 2}) of 14 hours, and we need to find the half-life when the substance is 10 g.

Understanding Half-Life Independence

The half-life of a substance depends solely on the properties of the substance and not on its quantity or mass. Therefore, whether it is 5 g or 10 g, the half-life remains the same.

Conclusion

Since the quantity of the substance does not affect its half-life, the half-life will remain 14 hours regardless of whether the sample is 5 g or 10 g.

Key concepts

Half-life

The concept of half-life is a central topic in understanding radioactive decay. Half-life refers to the time it takes for half of a given amount of a radioactive substance to decay. This means if you start with a certain amount, say 100 grams, after one half-life, you will have 50 grams remaining.
Half-life is an intrinsic property of a radioactive isotope, meaning it does not depend on external factors such as the amount of substance you have or external conditions like temperature or pressure. A critical point to remember is that the half-life remains constant regardless of the size of the sample.
In our exercise, whether you have 5 g or 10 g of the substance, the half-life is still 14 hours. This independence from quantity is what allows scientists to consistently use it to predict the decay pattern of a given substance. When learning about half-life, it is helpful to conduct simple experiments with simulations to visualize how the decay process occurs over time.

Radioactive Substances

Radioactive substances are materials that have unstable nuclei and tend to release radiation as they transform into more stable forms. This process is known as radioactive decay, and it continues until a stable form, often a different element, is achieved.
The radiation emitted can come in several forms, such as alpha particles, beta particles, or gamma rays. Each type of emission has different properties and levels of penetration power. Alpha particles, for instance, can be stopped by a sheet of paper, while gamma rays require heavier metal shielding.
In practical applications, understanding the characteristics of radioactive substances aids in developing safety protocols, medical treatments, and nuclear energy solutions. It is crucial to handle these substances with care and employ appropriate safety measures to protect humans and the environment from unnecessary exposure.

Nuclear Chemistry

Nuclear chemistry encompasses the study of reactions and processes that involve changes in atomic nuclei. It is a branch of chemistry that deals not just with radioactive decay, but also nuclear reactions and their applications.
Nuclear reactions are responsible for phenomena such as fission, where a heavy nucleus splits into two smaller nuclei, often used in nuclear power plants to generate energy, and fusion, which involves combining two light nuclei to form a heavier nucleus, a process that powers the sun.

• Fission: Involves large atoms, such as uranium or plutonium, where the nucleus splits into smaller parts, releasing tremendous amounts of energy.
• Fusion: Powers the sun; involves lighter nuclei like hydrogen atoms under extremely high temperatures and pressures.

Nuclear chemistry is critical in a variety of fields, from harnessing energy for electricity to medical applications like cancer treatment with radioactive isotopes. Understanding nuclear chemistry principles is essential for harnessing the benefits of radioactive materials safely and effectively.