Question

Complete and balance the nuclear equations for the following fission reactions: (a) \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{72} \mathrm{Zn}+{ }_{0}^{1} \mathrm{n}\) (b) \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{58}^{444} \mathrm{Ce}+\ldots+2{ }_{0}^{1} \mathrm{n}\)

Short answer

The balanced nuclear fission equations are: (a) \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{75} \mathrm{Zn}+{ }_{0}^{1} \mathrm{n}\) (b) \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{58}^{144} \mathrm{Ce}+{ }_{36}^{94} \mathrm{Kr}+2{ }_{0}^{1} \mathrm{n}\)

Step-by-step solution

Analyze the given equation

We are given a fission reaction involving Uranium: \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{72} \mathrm{Zn}+{ }_{0}^{1} \mathrm{n}\) First, let's analyze the left side of the equation: - Total atomic number: \(92 + 0 = 92\) - Total mass number: \(235 + 1 = 236\) Remember to keep these numbers in mind for the next step. #Step 2: Balancing the atomic and mass numbers#

Compare the numbers on both sides of the equation

Next, let's compare the numbers on both sides of the equation: - Total atomic number on the right side: \(62 + 30 + 0 = 92\) - Total mass number on the right side: \(160 + 72 + 1 = 233\) We can observe that the atomic numbers are balanced on both sides, however, the mass numbers are not balanced. There is a difference of 3 on the right side. #Step 3: Correcting the mass number of Zinc (Zn)#

Adjust the mass number of Zinc

To balance the mass numbers, let's adjust the mass number of Zinc: \(233 + 3 = 236\) Now, we can rewrite the corrected equation: \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{62}^{160} \mathrm{Sm}+{ }_{30}^{75} \mathrm{Zn}+{ }_{0}^{1} \mathrm{n}\) This nuclear fission equation is now balanced. #Step 4: Balancing the second nuclear fission equation#

Analyze the given equation

We are given another fission reaction involving Plutonium: \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{58}^{144} \mathrm{Ce}+\ldots+2{ }_{0}^{1} \mathrm{n}\) First, let's analyze the left side of the equation: - Total atomic number: \(94 + 0 = 94\) - Total mass number: \(239 + 1 = 240\) Remember to keep these numbers in mind for the next step. #Step 5: Determine the missing product's atomic and mass numbers#

Calculate the atomic and mass numbers of the missing product

Now we'll determine the missing product's atomic and mass numbers. First, let's calculate the atomic number: \(94 - 58 = 36\) Thus, the atomic number of the missing product is 36, which corresponds to Krypton (Kr). Now, let's determine the mass number: \(240 - 144 - 2(1) = 94\) The mass number of the missing krypton isotope is 94. Now, we can fill in the missing product: \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{58}^{144} \mathrm{Ce}+{ }_{36}^{94} \mathrm{Kr}+2{ }_{0}^{1} \mathrm{n}\) This nuclear fission equation is now balanced.

Key concepts

Understanding Nuclear Chemistry

Nuclear chemistry is a fascinating and critical area of study that deals with the changes in the nucleus of atoms. While chemistry typically deals with reactions involving electrons, nuclear chemistry focuses on processes such as nuclear fission, fusion, and radioactive decay. As we delve into understanding this topic, it's imperative to comprehend the nature of the atomic nucleus, isotopes, and the concept of nuclear stability.

Atoms consist of a nucleus, containing protons and neutrons, surrounded by electrons. Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons, leading to variations in mass. Some isotopes are unstable and may undergo spontaneous transformations to achieve a more stable configuration. This is at the heart of nuclear reactions, where the nucleus of an atom changes and can release or absorb an enormous amount of energy.

Understanding nuclear chemistry is not only academically intriguing, but also has practical implications, such as in the generation of nuclear energy, medical imaging, and treatment, as well as in understanding environmental radiation.

Balancing Nuclear Reactions

Balancing nuclear reactions is essential for accurately describing the transformation of nuclear particles during a reaction. A balanced nuclear equation respects the conservation laws of physics, specifically the conservation of mass and atomic number. In a balanced equation, the sum of atomic numbers and mass numbers must be the same on both sides of the equation.

The process of balancing nuclear reactions involves identifying the reactants and products, and ensuring that the sums of their atomic numbers (the number of protons, denoted as the lower subscript) and mass numbers (the sum of protons and neutrons, denoted as the upper subscript) are equal. If there's a discrepancy, like in the examples provided, adjustments are made to the reactants or products until both conservation laws are satisfied. Steps like these ensure that the nuclear reactions align with our understanding of physical laws and enable us to predict the results of such reactions with accuracy.

Identifying Nuclear Fission Products

Nuclear fission is a type of nuclear reaction in which a heavy nucleus, when bombarded by neutrons, splits into smaller nuclei, additional neutrons, and a significant amount of energy. The exercise provided illustrates uranium-235 and plutonium-239 undergoing fission. Identifying fission products is key to understanding the result of a fission reaction, and it involves more than just determining the elements formed. It includes recognizing the isotopes produced, their stability, and the amount of energy released.

In a fission reaction like the ones in the exercise, mass and atomic numbers must be meticulously accounted for to predict the products correctly. The products can include various combinations of lighter elements, as well as the release of additional neutrons that can perpetuate the fission process. This is critical for applications such as nuclear reactors, where the chain reaction of fission events is harnessed to produce energy. By executing the steps provided, students can learn to predict fission products and understand the significant role fission plays in both natural phenomena and engineered systems.