Problem 16 - Chemistry Matter and Change

Question

Calculate how much of a 10.0 -g sample of americium-241 remains after four half-lives. Americium- 241 is a radioisotope commonly used in smoke detectors and has a half-life of 430 y.

Step-by-Step Solution

Answer

0.625 g of americium-241 remains after four half-lives.

Step 1: Understanding Half-Life

The half-life of a substance is the time it takes for half of the radioactive atoms in a sample to decay. In this problem, americium-241 has a half-life of 430 years. We need to calculate the remaining mass after four half-lives.

Step 2: Calculating Total Time Elapsed

Since each half-life is 430 years, we multiply the half-life by the number of half-lives that have passed to find the total time elapsed. Therefore, the total time is \(4 \times 430\) years, which equals 1720 years.

Step 3: Initial Mass

The initial mass of the americium-241 sample is given as 10.0 g. We will use this initial mass to calculate the remaining mass after multiple half-lives.

Step 4: Decay Calculation

With each half-life, the amount of americium-241 remaining is halved. After one half-life, 5.0 g remains. After two half-lives, 2.5 g remains. After three half-lives, 1.25 g remains. After four half-lives, we calculate \(\frac{1.25}{2} = 0.625\) g remaining.

Key Concepts

Radioactive Decay

Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This decay happens spontaneously and results in the formation of new, more stable nuclei.
The rate of this decay is characteristic to each radioactive isotope and is measured by its half-life, which is the time required for half of the radioactive nuclei to decay.

• Highly significant in nuclear chemistry as it helps in understanding the time a radioactive substance will remain active.
• Radioactive decay processes include alpha decay, beta decay, and gamma decay.

The math involved in decay calculations often utilizes the half-life to determine how much of a substance remains over time.

Americium-241

Americium-241 is a radioactive isotope commonly used in commercial smoke detectors and various industrial applications. This element is created in nuclear reactors and is part of the actinide series on the periodic table.
Americium-241 undergoes alpha decay to transform into neptunium-237.

• It has a relatively long half-life of 430 years, making it a stable choice for devices that require long-term efficiency.
• Its decay process not only helps in smoke detection by emitting alpha particles but also produces gamma radiation in small amounts.

Understanding the use of americium-241 in practical applications exemplifies the intersection of nuclear chemistry and day-to-day technology.

Nuclear Chemistry

Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, and properties. It encompasses the study of both natural and man-made radioactive compounds.
Key concepts in nuclear chemistry include radioactive decay, fission, fusion, and the effects of radiation on matter.

• Radioactive isotopes like americium-241 are crucial for applications ranging from medical diagnostics to energy production.
• It also involves the transformation of elements and isotopes through nuclear reactions and radioactive decay processes.

Through nuclear chemistry, scientists can harness the energy stored in the nucleus of atoms, allowing for advances in fields such as medicine, energy, and environmental science.