Question

The diagram shown here illustrates a fission process. \begin{equation} \begin{array}{l}{\text { (a) What is the unidentified product of the fission? }} \\ {\text { (b) Use Figure } 21.2 \text { to predict whether the nuclear products }} \\ \quad {\text { of this fission reaction are stable. [ Section } 21.7 ]}\end{array} \end{equation}

Short answer

In summary, to identify the unknown product in a fission process, apply the conservation of mass number and conservation of atomic number equations to find its atomic number and mass number. For example, with a given fission process \(\ce{^{A_1}_{Z_1}X + ^{1}_{0}n -> ^{A_2}_{Z_2}Y + ^{A_3}_{Z_3}Z + 2 ^{1}_{0}n}\), solve \( A_1 + 1 = A_2 + A_3 \) and \( Z_1 + 0 = Z_2 + Z_3 \) for the unknown product X. Next, consult Figure 21.2 to determine the stability of the nuclear products. If they lie on or near the stability curve, they are stable; otherwise, they will be unstable or radioactive.

Step-by-step solution

Analyzing the given fission process

Analyze the fission process diagram which should consist of a certain nucleus undergoing fission and the products after the fission. Identify the unknown product by using its symbol, such as X. Also, identify the other products and the initial nucleus. Consider an example where the fission process is as follows: \[\ce{^{A_1}_{Z_1}X + ^{1}_{0}n -> ^{A_2}_{Z_2}Y + ^{A_3}_{Z_3}Z + 2 ^{1}_{0}n}\] Here, X is the initial nucleus, Y and Z are the fission products, and n is a neutron.

Applying conservation laws to find the unidentified product

Apply conservation of mass number and conservation of atomic number in the fission process: 1. Conservation of mass number (number of protons and neutrons): The sum of mass numbers on the left side is equal to the sum of mass numbers on the right side. \( A_1 + 1 = A_2 + A_3 \) 2. Conservation of atomic number (number of protons): The sum of atomic numbers on the left side is equal to the sum of atomic numbers on the right side. \( Z_1 + 0 = Z_2 + Z_3 \) Now, using the given nucleus Y and Z's atomic number and mass number, solve for the unknown product X's atomic number and mass number, which will give you the complete identity of the unknown fission product.

Consult Figure 21.2 to determine if the products are stable or not

Now that we have identified our nuclear products, refer to Figure 21.2 to determine whether the products are stable or not. Look at the stability curve and locate the identified nuclear products. If the products lie close to or on the stability curve, they are stable. If they lie away from the stability curve, they will be unstable or radioactive. #Conclusion# Following the steps given above, a student should be able to identify an unknown nuclear product in a fission process and determine its stability using Figure 21.2. The most important part in solving this problem is applying the conservation laws wisely to find the unknown product.

Key concepts

Conservation Laws

In nuclear fission, conservation laws play a critical role in identifying unknown products and understanding the reaction. There are two fundamental conservation laws that you need to focus on.

• Conservation of Mass Number: The sum of the mass numbers (total number of protons and neutrons) on both sides of the nuclear reaction must be equal. For example, if the initial nucleus and a neutron produce two fission products, their combined mass numbers must add up to the mass number of the initial nucleus plus the neutron. Mathematically, if the initial mass number is represented by \( A_1 \), and the mass numbers of the products are \( A_2 \) and \( A_3 \), then:\[A_1 + 1 = A_2 + A_3\]


• Conservation of Atomic Number: This law states that the sum of the atomic numbers (number of protons) on both sides of the equation must remain equal. Therefore, the atomic number of the unidentified product can be found by balancing the atomic numbers of all products, typically represented as:\[Z_1 + 0 = Z_2 + Z_3\]

By applying these conservation principles, one can solve for unknown nuclear products in a fission process.

Stability of Nuclear Products

After identifying the nuclear products of a fission reaction, the next step is to determine their stability. Stability in this context means that the nucleus does not undergo further spontaneous transformations.

The stability of a nuclear product can be judged by consulting a chart such as Figure 21.2, which typically represents a stability curve. Here’s how to check the stability based on the position on this curve:

• On or Near the Stability Curve: Products that lie on or near the curve are generally stable. The curve usually represents the balance between protons and neutrons that leads to stable nuclei.
• Away From the Curve: If a nuclear product is far away from this curve, it is likely unstable and may undergo radioactive decay to achieve a more stable state.

Therefore, using such a figure, one can easily assess whether the products of the nuclear fission are stable or potentially radioactive.

Fission Processes

Nuclear fission is a process where a heavy nucleus, when struck by a neutron, splits into lighter nuclei along with additional neutrons and energy release. This process is crucial in both energy generation and understanding nuclear reactions.

Let's explore the core aspects:

• Initial Reaction: A typical fission process begins with a neutron colliding with a heavy nucleus, leading to its excitation and eventual splitting into more stable, smaller nuclei. For instance, a uranium-235 nucleus hit by a neutron might split into barium, krypton, and more neutrons.
• Chain Reaction: The emitted neutrons can trigger further fission reactions in nearby nuclei, leading to a self-sustaining chain reaction crucial for nuclear reactors and atomic explosions.
• Energy Release: A vast amount of energy is released during fission because the combined mass of the fission products is less than the original mass, with the difference converted into energy as per Einstein's equation \( E=mc^2 \).

Understanding these processes is key for both managing nuclear energy and developing safety protocols in nuclear technology.