Problem 52 - Chemistry: An Atoms-Focused Approach

Question

Bombardment of a \({ }^{239} \mathrm{Pu}\) target with \(\alpha\) particles produces \({ }^{242} \mathrm{Cm}\) and another particle. a. Use a balanced nuclear equation to determine the identity of the missing particle. b. The synthesis of which other nuclide described in this chapter involves the same subatomic particles?

Step-by-Step Solution

Answer

Question: Write a balanced nuclear equation for the bombardment of Plutonium-239 with alpha particles, determine the identity of the missing particle, and find another described nuclide that involves the same subatomic particles. Answer: The balanced nuclear equation for the bombardment of Plutonium-239 with alpha particles is ²³⁹Pu + α → ²⁴²Cm + n. The missing particle is a neutron (n). Another nuclide involving the same subatomic particles is the synthesis of Plutonium-240 (²⁴⁰Pu) through neutron capture and decay: ²³⁹Pu + n → ²⁴⁰Pu and ²⁴⁰Pu → ²⁴⁰Am + α.

Step 1: Write the nuclear bombardment reaction

Write the given bombardment reaction: ²³⁹Pu + α → ²⁴²Cm + X Here X is the missing particle. - ²³⁹Pu represents Plutonium-239. - α represents the alpha particle.

Step 2: Find the missing particle's mass and atomic numbers

An alpha particle has a mass number of 4 and an atomic number of 2. Therefore, we need to find the mass and atomic numbers of the missing particle X so that the equation is balanced. To balance the mass numbers: A1 + A2 = A3 + A4 And to balance the atomic numbers: Z1 + Z2 = Z3 + Z4 Where, - A1 = Mass number of Pu = 239 - A2 = Mass number of α = 4 - A3 = Mass number of Cm = 242 - Z1 = Atomic number of Pu = 94 - Z2 = Atomic number of α = 2 - Z3 = Atomic number of Cm = 96 Find A4 and Z4 using the balanced equations: A4 = A1 + A2 - A3 = 239 + 4 - 242 = 1 Z4 = Z1 + Z2 - Z3 = 94 + 2 - 96 = 0 Therefore, the missing particle has a mass number of 1 and an atomic number of 0.

Step 3: Identify the missing particle

From the balanced equations, we found that the missing particle has a mass number of 1 and an atomic number of 0. The particle with these properties is a neutron (n). So the balanced nuclear reaction equation is: ²³⁹Pu + α → ²⁴²Cm + n b. Synthesis of another nuclide involving the same subatomic particles:

Step 4: Identifying a similar nuclide synthesis

To complete this task, the nuclide synthesis should involve the Plutonium-239 (²³⁹Pu) target, alpha particles, and neutrons. One similar nuclide is the synthesis of Plutonium-240 (²⁴⁰Pu) through neutron capture and decay. The reaction is as follows: 1. ²³⁹Pu + n → ²⁴⁰Pu (Neutron capture) 2. ²⁴⁰Pu → ²⁴⁰Am + α (Alpha decay) In this synthesis mechanism, the same subatomic particles (alpha particles and neutrons) are involved in the process.

Key Concepts

Alpha Particles

Alpha particles are a type of ionizing radiation ejected by the nuclei of some unstable atoms. These particles consist of two protons and two neutrons, giving them a helium-4 nucleus structure. Alpha particles are represented by the symbol \(\alpha\) and have:

• A mass number of 4, due to the two protons and two neutrons.
• An atomic number of 2, because of the two protons.

In nuclear reactions, alpha particles are often used to bombard other elements to produce new isotopes or elements. For example, in the provided exercise, an alpha particle bombards Plutonium-239 \(({}^{239} \mathrm{Pu})\), which results in the production of Curium-242 \(({}^{242} \mathrm{Cm})\) as well as another particle. This is a classic example of nuclear transmutation where the target nucleus absorbs the alpha particle's components and transforms into a different element.

Neutron Capture

Neutron capture is a nuclear process in which a nucleus captures one or more free neutrons. This process can lead to the creation of heavier isotopes or entirely new elements. Neutrons, being electrically neutral, do not face the repulsive forces that charged particles encounter, allowing them to penetrate nuclei easily.
The importance of neutron capture extends into various fields, including:

• Nuclear reactor operations, where it helps sustain nuclear chain reactions.
• Astrophysics, where it contributes to the formation of heavy elements in stars.

In our example, neutron capture is relevant when discussing the synthesis of Plutonium-240 \(({}^{240} \mathrm{Pu})\). Here, a neutron combines with Plutonium-239, leading to the creation of a new nuclide. This showcases how neutron capture can lead to element transmutation and has important applications in both energy generation and scientific research.

Balanced Nuclear Equations

A balanced nuclear equation ensures that the total atomic and mass numbers remain constant before and after a nuclear reaction. To balance these equations:

• The sum of the atomic numbers (protons in the nucleus) on both sides of the equation should be equal.
• The sum of the mass numbers (total protons and neutrons) must also be matched on both sides.

For the exercise given, balancing the nuclear reaction involves identifying a missing particle in the equation \( {}^{239} \mathrm{Pu} + \alpha \rightarrow {}^{242} \mathrm{Cm} + X \). As calculated, the mass number of the missing particle \( X \) is 1, and its atomic number is 0, which corresponds to a neutron \((n)\).
Balanced nuclear equations are fundamental in understanding nuclear processes and ensuring the proper accounting of all particles involved in reactions. Without this balance, important details about changes in nuclear composition or possible isotopes might be overlooked.