Problem 20 - Introductory Chemistry Atoms First

Question

Complete this nuclear reaction, and state whether it is fission or fusion. $$ { }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{38}^{90} \mathrm{Sr}+?+3{ }_{0}^{1} \mathrm{n} $$

Step-by-Step Solution

Answer

The complete nuclear reaction is: \( { }_{94}^{239} \mathrm{Pu} + { }_{0}^{1} \mathrm{n} \rightarrow{ }_{38}^{90} \mathrm{Sr} + { }_{56}^{150} \mathrm{Ba} + 3{ }_{0}^{1} \mathrm{n} \) And the type of nuclear reaction is fission.

Step 1: Apply conservation of mass number and atomic number

We will first apply the conservation of mass number (A) and atomic number (Z). \( A_{1} + A_{2} = A_{3} + A_{4} \) Also, \( Z_{1} + Z_{2} = Z_{3} + Z_{4} \) So, for this reaction: \( 239 + 1 = 90 + A_{4} \) \( 94 + 0 = 38 + Z_{4} \)

Step 2: Find the missing product's mass number and atomic number

Now, we'll solve the equations from Step 1 to find the missing product's mass number (A_4) and atomic number (Z_4). Mass number equation: \( A_{4} = 239 + 1 - 90 = 150 \) Atomic number equation: \( Z_{4} = 94 - 38 = 56 \) Now, we know the missing product's mass number and atomic number: \( { }_{56}^{150} \mathrm{X} \)

Step 3: Identify the missing product by atomic number

By looking at the periodic table, we'll find that the element with atomic number 56 is Barium (Ba). Therefore, the missing product is: $$ { }_{56}^{150} \mathrm{Ba} $$

Step 4: Identify the type of reaction as fission or fusion

Now, we'll determine if the reaction is fission or fusion. A fission reaction involves splitting a heavy nucleus into lighter nuclei, while fusion involves combining lighter nuclei to form a heavier nucleus. In this case, the plutonium nucleus ("\(_{94}^{239}\mathrm{Pu}\)") is heavy and it splits into lighter elements ("\(_{38}^{90}\mathrm{Sr}\)" and "\(_{56}^{150}\mathrm{Ba}\)"), so this reaction is an example of nuclear fission.

Step 5: Final Answer

The complete nuclear reaction is: $$ { }_{94}^{239} \mathrm{Pu} + { }_{0}^{1} \mathrm{n} \rightarrow{ }_{38}^{90} \mathrm{Sr} + { }_{56}^{150} \mathrm{Ba} + 3{ }_{0}^{1} \mathrm{n} $$ And the type of nuclear reaction is fission.

Key Concepts

Nuclear Reaction

A nuclear reaction involves the transformation of the nucleus of an atom. It occurs when subatomic particles such as protons and neutrons, which reside in the nucleus of an atom, are rearranged. In our exercise, the nuclear reaction involves plutonium (Pu) and a neutron (n) reacting to form strontium (Sr), barium (Ba), and additional neutrons. The two main types of nuclear reactions are fission and fusion.

• **Fission** is when a heavy nucleus splits into smaller, lighter nuclei, releasing energy.
• **Fusion** is when light nuclei combine to form a heavier nucleus, also releasing energy.

Differentiating between these reaction types is crucial because the processes and applications, such as energy production, differ vastly.

Mass Number Conservation

Mass number conservation is one of the essential principles governing nuclear reactions. The mass number (A) is the total number of protons and neutrons in the nucleus. This principle states that the total mass number before the reaction must equal the total mass number after the reaction.
In our example:

• Mass number of reactants: 239 (Pu) + 1 (n) = 240.
• Mass number of products: 90 (Sr) + 150 (Ba) + 3 (n) = 240.

This equality demonstrates that mass number is conserved during the nuclear reaction.

Atomic Number Conservation

Atomic number conservation is another critical principle in nuclear reactions. The atomic number (Z) is the number of protons in the nucleus and defines the element's identity in the periodic table.

• The sum of atomic numbers of reactants will equal the sum of atomic numbers of products.

For our exercise, we have:

• Atomic number of reactants: 94 (Pu) + 0 (n) = 94.
• Atomic number of products: 38 (Sr) + 56 (Ba) = 94.

This conservation ensures the same elements exist on both sides of the reaction, maintaining elemental balance.

Isotopes

Isotopes are atoms that have the same number of protons but differ in the number of neutrons. This variation in neutron number affects the mass number but not the atomic number, which remains constant for isotopes of a single element.
Understanding isotopes is critical in nuclear chemistry because isotopes can differ drastically in stability and reactivity.

• For instance, plutonium-239 ( _{94}^{239} Pu) is an isotope with 94 protons and 145 neutrons.
• It can undergo fission reactions releasing significant energy.

Periodic Table

The periodic table is a systematic arrangement of elements based on their atomic number, electron configuration, and recurring chemical properties. Each element is represented by its atomic number, symbol, and atomic mass.
In nuclear chemistry, the periodic table helps identify elements and isotopes involved in reactions.

• In our exercise, we determine that the element with atomic number 56 is Barium (Ba).
• The periodic table aids in verifying the identity and properties of nuclear reaction products.

Understanding the periodic table allows predictions about bonding, reactivity, and the behavior of different elements in nuclear reactions.