Problem 20 - Chemistry Matter and Change

Question

Write the balanced nuclear equation for the alpha-particle bombardment of \(_{94}^{239} \mathrm{Pu}\) . One of the reaction products is a neutron.

Step-by-Step Solution

Answer

The balanced nuclear equation for the alpha-particle bombardment of \(_{94}^{239}\mathrm{Pu}\) with one neutron as a reaction product is: \[_{94}^{239}\mathrm{Pu} + _2^4\mathrm{He} \rightarrow _0^1\mathrm{n} + _{96}^{242}\mathrm{Cm} \]

Step 1: Identify projectile and target nuclei

The target nucleus is given as \(_{94}^{239}\mathrm{Pu}\). The projectile is an alpha particle, which is a helium nucleus, represented as \(_2^4\mathrm{He}\). #Step 2: Write the nuclear equation without the missing product#

Step 2: Write incomplete nuclear equation

Now, we can write the nuclear equation without the missing product: \[_{94}^{239}\mathrm{Pu} + _2^4\mathrm{He} \rightarrow _0^1\mathrm{n} + ? \] #Step 3: Find the atomic number and mass number of the missing product#

Step 3: Calculate atomic number and mass number for the missing product

In order to find the missing product, we need to conserve both mass numbers and atomic numbers. Let's denote the atomic number of the missing product as Z and the mass number as A. To conserve atomic numbers: \(94 + 2 = 0 + Z \Rightarrow Z = 96\) To conserve mass numbers: \(239 + 4 = 1 + A \Rightarrow A = 242\) #Step 4: Identify the element with the atomic number 96#

Step 4: Identify element with atomic number 96

The element with atomic number 96 is curium (Cm). The missing product is \(_{96}^{242}\mathrm{Cm}\). #Step 5: Write the balanced nuclear equation#

Step 5: Write balanced nuclear equation

Now we can write the complete balanced nuclear equation: \[_{94}^{239}\mathrm{Pu} + _2^4\mathrm{He} \rightarrow _0^1\mathrm{n} + _{96}^{242}\mathrm{Cm} \]

Key Concepts

Alpha-Particle Bombardment

Alpha-particle bombardment involves using alpha particles to initiate a nuclear reaction. An alpha particle is essentially a helium nucleus, with two protons and two neutrons, represented as \(_2^4\mathrm{He}\). In nuclear reactions, alpha particles are used to collide with target nuclei and create new elements.
This process can be visualized as a tiny particle striking a larger one, leading to the formation of different elements or isotopes.

• The bombardment can transform one type of atom into another.
• It is a fundamental technique in nuclear chemistry and physics.

By understanding alpha-particle bombardment, we can explore how elements can change and how new elements are discovered.

Mass Number Conservation

Mass number conservation ensures that the total mass number (sum of protons and neutrons) remains the same before and after a nuclear reaction.
In a nuclear equation, you add the mass numbers of the reactants and ensure they equal the mass numbers of the products.

• If we have \(239 + 4\), which equals \(243\) on the reactant side, it should equal the total on the product side, say \(242 + 1\).
• This balance helps to determine unknown components in nuclear reactions.

Mass number conservation is fundamental in safely predicting the outcomes and balancing nuclear equations.

Atomic Number Conservation

Atomic number conservation maintains that the total atomic number (equivalent to the number of protons) stays constant throughout a nuclear reaction. This helps identify the missing elements or isotopes in reactions.
For example, if you start with an atomic number of \(94 + 2\) in a reaction, this should match the sum of atomic numbers on the product side, like \(96 + 0\).

• Ensures that no protons are lost or unaccounted for during reactions.
• Provides clarity on potential element transformations.

Atomic number conservation is essential for accurately balancing nuclear equations and ensuring that all atomic identities remain consistent.

Curium

Curium is a synthetic and radioactive element with an atomic number of 96. It was discovered as a result of such nuclear reactions as alpha-particle bombardment. Named after Marie and Pierre Curie, it is part of the actinide series.

• Curium typically appears in research and reactor fuel assemblies.
• Its most common isotopes are used in space missions for power generation.

Understanding curium and its properties helps chemists and physicists explore new possibilities in space technology and nuclear energy.

Neutron

Neutrons are neutral particles found in the nucleus of an atom, playing a key role in the stability of atoms. In nuclear reactions, they might appear as one of the byproducts.
In the given reaction, one neutron \(_0^1\mathrm{n}\) is produced along with curium.

• Neutrons help balance mass and facilitate the binding of protons within the nucleus.
• They are crucial in chain reactions, like those in nuclear reactors.

Understanding neutrons is fundamental in both nuclear chemistry and physics, as they contribute to the understanding of atomic structures and reactions.