Question

The half=life period of radium is 1580 years. It remains \(1 / 16\) after how many years? (a) 1580 years (b) 3160 years (c) 4740 years (d) 6320 years

Short answer

6320 years.

Step-by-step solution

Understand the Problem

We are given the half-life of radium as 1580 years. We need to find out how many years it will take for a quantity of radium to reduce to \(\frac{1}{16}\) of its original amount.

Recognize the Pattern

Each half-life period reduces a quantity to half of its original amount. The key here is to determine how many times the radium must be halved to reach \(\frac{1}{16}\) of its original amount.

Calculate the Number of Half-lives

Since it reduces to \(\frac{1}{16}\), we need to express \(\frac{1}{16}\) as a power of \(\frac{1}{2}\) because each half-life reduces the quantity to half. Therefore, \[\frac{1}{16} = \left(\frac{1}{2}\right)^4\]. This means four half-lives are needed.

Multiply the Number of Half-lives by the Half-life Period

If each half-life period is 1580 years, and 4 half-life periods are needed, we calculate the total time as \(4 \times 1580 = 6320\) years.

Key concepts

Understanding Half-Life

Half-life is an important concept in nuclear chemistry. It refers to the time it takes for half of a radioactive substance to decay. This doesn't mean the material has disappeared but that its activity has reduced by half. For example, if you start with 100 grams of a substance with a half-life of 1580 years, after 1580 years, only 50 grams will remain active. After another 1580 years, only 25 grams would be left, and so on.

Half-life helps us understand how quickly or slowly a substance will decay over time. It is crucial in fields like archaeology, where the decay of carbon isotopes helps date artifacts, or in medicine, where the decay of radioactive isotopes is used in diagnostic imaging.

• Half-life measures the rate of decay of a substance.
• A consistent and predictable pattern of decay helps in planning and safety in nuclear applications.
• It applies to any quantity of a radioactive substance, from grams to kilograms.

The Role of Radium in Radioactive Decay

Radium is a well-known radioactive element with an atomic number of 88. It is found in trace amounts in uranium and thorium ores. Radium itself decays into radon gas, which is also radioactive. Its half-life is 1580 years, meaning it takes this long for half of any sample of radium to decay into radon.

Radium was used in early 20th-century luminous paints for watches, aircraft switches, and clock faces because of its ability to glow in the dark. However, due to its radioactive properties, its use has declined due to potential health risks. Handling radium requires careful measures to avoid radiation exposure.

• Radium decays into radon, a radioactive gas.
• It was historically used in glow-in-the-dark paints.
• Radium highlights the need for safety in handling radioactive materials.

An Introduction to Nuclear Chemistry

Nuclear chemistry involves the study of radioactive substances and their reactions. It examines how atoms decay, transform, and release energy. This field has vital applications, from nuclear power generation to medical treatments.

A key part of nuclear chemistry is understanding isotopes, variants of elements with different neutron numbers. Some isotopes are stable, while others, like radium, are unstable and radioactive. Radioactive isotopes decay over time, releasing particles and energy in the process.

• Nuclear chemistry deals with reactions and properties of radioactive materials.
• It explores the benefits and risks of radioactive substances in various fields.
• Isotopes are central to nuclear chemistry, with their stability determining their behavior.

With advancements in technology, nuclear chemistry continues to provide significant insights and innovations, such as improving nuclear waste disposal methods and developing less invasive medical diagnostic tools.