Problem 39 - Chemistry and Chemical Reactivity

Question

Americium-240 is made by bombarding plutonium-239 with \(\alpha\) particles. In addition to \(^{240} \mathrm{Am}\), the products are a proton and two neutrons. Write a balanced equation for this process.

Step-by-Step Solution

Answer

The balanced equation is: \( ^{239}_{94} \mathrm{Pu} + ^{4}_{2} \mathrm{He} \rightarrow ^{240}_{95} \mathrm{Am} + ^{1}_{1} \mathrm{H} + 2 ^{1}_{0} n \).

Step 1: Understanding the Reaction Components

The reaction starts with bombarding plutonium-239 \(( ^{239}_{94} \mathrm{Pu})\) with alpha particles \(( ^{4}_{2} \mathrm{He})\). The reaction produces americium-240 \(( ^{240}_{95} \mathrm{Am})\), a proton \(( ^{1}_{1} \mathrm{H})\), and two neutrons \(( ^{1}_{0} n)\).

Step 2: Setting Up the Reaction Equation

In a nuclear reaction, both the atomic number and the mass number must be balanced. This means determining a balanced equation with the reactants \(( ^{239}_{94} \mathrm{Pu} + ^{4}_{2} \mathrm{He})\) and the products \(( ^{240}_{95} \mathrm{Am} + ^{1}_{1} \mathrm{H} + 2\times ^{1}_{0} n)\).

Step 3: Balancing the Mass Numbers

Check the sum of the mass numbers on both sides. On the left, we have \(239 + 4 = 243\). On the right, \(240 + 1 + 2\times1 = 243\). The mass numbers balance.

Step 4: Balancing the Atomic Numbers

Check the sum of the atomic numbers on each side. On the left, the atomic numbers are \(94 + 2 = 96\). On the right, they add up to \(95 + 1 + 0 = 96\). The atomic numbers also balance.

Step 5: Writing the Balanced Equation

With both mass and atomic numbers balanced, the equation for the reaction is: \( ^{239}_{94} \mathrm{Pu} + ^{4}_{2} \mathrm{He} \rightarrow ^{240}_{95} \mathrm{Am} + ^{1}_{1} \mathrm{H} + 2 ^{1}_{0} n \).

Key Concepts

Alpha Particle Bombardment

In nuclear physics, alpha particle bombardment is a fascinating process. It involves shooting alpha particles, which are essentially helium nuclei, at a target nucleus. Here, these helium nuclei are represented as \( ^{4}_{2} \mathrm{He}\).

• An alpha particle is composed of 2 protons and 2 neutrons, giving it a mass number of 4.
• The atomic number of an alpha particle is 2, corresponding to its 2 protons.

In the exercise, plutonium-239 is bombarded with these tiny, high-energy particles. This bombardment can cause a reaction that usually transforms the target nucleus by either fusing or causing it to split, leading to new elements or isotopes. Understanding this helps explain how americium-240 is produced in the given nuclear reaction.

Balancing Nuclear Equations

Balancing nuclear equations is crucial to understanding and representing nuclear reactions accurately. Like chemical equations, nuclear equations must adhere to certain balance rules:

• Conservation of mass number (sum of mass numbers before and after the reaction must be equal).
• Conservation of atomic number (sum of atomic numbers before and after the reaction must be equal).

In the example given, you begin with plutonium-239 and helium (an alpha particle) and end with americium-240, a proton, and two neutrons. Each component and its position in the equation affect the overall balance. This ensures that no matter how complex the nuclear reactions get, they can be systematically understood and depicted using these balance principles. Mastery of these principles aids a deeper understanding of more complex nuclear phenomena.

Atomic Numbers

The atomic number is a fundamental aspect of an atom's identity. It represents the number of protons in the nucleus of an atom and determines which element the atom belongs to. In nuclear reactions, the atomic number must remain conserved.

For instance, in our nuclear reaction:

• Plutonium (\( ^{239}_{94} \mathrm{Pu}\)) has an atomic number of 94.
• The alpha particle (\( ^{4}_{2} \mathrm{He}\)) has an atomic number of 2.
• Americium (\( ^{240}_{95} \mathrm{Am}\)) has an atomic number of 95.
• The proton (\( ^{1}_{1} \mathrm{H}\)) has an atomic number of 1.

Understanding and working with atomic numbers helps to ensure that equations are balanced, making it a fundamental step in writing and verifying nuclear equations.

Mass Numbers

Mass numbers are another key component of nuclear reactions. They provide the total count of protons and neutrons in an atom's nucleus.

• Plutonium-239 has a mass number of 239.
• The alpha particle has a mass number of 4.
• Americium-240 has, naturally, a mass number of 240.
• Each neutron has a mass number of 1, and so does the proton.

Balancing these mass numbers in nuclear reactions ensures the conservation of mass-energy in the reaction. This is one of the most vital steps in deriving a balanced nuclear equation. In any nuclear equation, the total mass number on the reactant side should equal the total mass number on the product side.