Problem 11 - Chemistry and Global Awareness

Question

Fatman (Nagasaki bomb) used approximately \(6.4 \mathrm{~kg}\) of Pu-239. This artificially produced isotope \(\left(\mathrm{t}_{1 / 2}=24,100\right.\) years) undergoes alpha decay. How many kg and pounds would remain after three decay processes?

Step-by-Step Solution

Answer

After three decay processes, 0.8 kg or 1.7637 pounds of Pu-239 remain.

Step 1: Understand the Half-life Concept

A half-life is the time required for half of a sample of a radioactive substance to decay. For Pu-239, the half-life is 24,100 years. We use this concept to determine how much of the substance remains after a certain number of decay processes.

Step 2: Determine the Remaining Fraction after Each Decay

After one half-life, half of the radioactive material will remain. Therefore, after three half-lives (24,100 years times 3), the remaining fraction of the original substance is \( \left( \frac{1}{2} \right)^3 = \frac{1}{8} \).

Step 3: Calculate the Remaining Mass in Kilograms

Originally, there are 6.4 kg of Pu-239. After three decay processes, \( \frac{1}{8} \) of the original mass remains. So, the remaining mass \( M \) is calculated as: \[ M = 6.4 imes \frac{1}{8} = 0.8 \text{ kg} \].

Step 4: Convert Kilograms to Pounds

To convert from kilograms to pounds, we use the conversion factor: 1 kg = 2.20462 pounds. Thus, the remaining mass in pounds is:\[ 0.8 \times 2.20462 = 1.7637 \text{ pounds} \].

Key Concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle. An alpha particle consists of two protons and two neutrons, essentially making it a helium nucleus. This process reduces the atomic number by 2 and the mass number by 4. During alpha decay:

• A parent nucleus emits an alpha particle.
• The parent atom changes into a different element due to the loss of protons.
• It is a common decay mode for heavy, radioactive nuclei.

This transformation is a way for unstable isotopes, like Pu-239, to release energy and become more stable. This decrease in mass and atomic number changes the composition of the element, often transforming it into a completely different element in the periodic table.

Pu-239

Pu-239, or Plutonium-239, is a man-made isotope extensively used in the context of nuclear physics and warfare. It is notable for its application in nuclear weapons and reactors.

• Pu-239 has an atomic number of 94 and a mass number of 239.
• This isotope is fissile, meaning it can sustain a nuclear chain reaction after absorbing neutrons.
• Its long half-life of 24,100 years makes it a durable source of energy emissions.

Despite its crucial role in history, the use of Pu-239 poses significant health, safety, and environmental risks due to its high radioactivity and long-lived nature.

Radioactive Decay Process

The radioactive decay process refers to the transformation of an unstable atomic nucleus into a more stable one. This process involves the emission of radiation in the form of particles or electromagnetic waves. There are different types of decay:

• Alpha decay, where an alpha particle is released.
• Beta decay, involving the transformation of a neutron into a proton with the emission of an electron.
• Gamma decay, which involves the release of electromagnetic radiation known as gamma rays.

Each kind of decay reduces nuclear instability and transforms the initial element into another element or isotope. These decay processes are crucial to understanding nuclear reactions, energy emissions, and the resulting changes in matter over time.

Mass Conversion

Mass conversion in the context of radioactive decay often involves converting the remaining mass of a substance into different units, using established conversion factors. This is essential when calculating quantities in scientific and engineering contexts. For instance:

• Once the remaining mass after decay has been calculated, it is common to convert mass units (e.g., kilograms to pounds).
• Conversions require use of standard conversion factors, such as 1 kg equating to 2.20462 pounds.
• Accurate mass conversions ensure correct measurements and are crucial for applications involving precise scientific and technical requirements.

Understanding mass conversion can also help illustrate the practical implications of radioactive decay, such as how much material will be left over time and how it is quantified in different systems of measurement.