Question

Would fusing two \({ }^{56} \mathrm{Fe}\) atoms together to produce \({ }^{112}\) Te be an exothermic reaction or an endothermic reaction? Justify your answer. (Hint: Don't do a calculation, just consult the plot of binding energy versus number of nucleons in the nucleus.)

Short answer

The fusion of two \(^{56}\mathrm{Fe}\) atoms to produce \(^{112}\mathrm{Te}\) would be an endothermic reaction. This is because the plot of binding energy per nucleon versus the number of nucleons in the nucleus shows that the binding energy per nucleon for \(^{112}\mathrm{Te}\) is lower than that of \(^{56}\mathrm{Fe}\). This indicates that the reaction requires energy to occur.

Step-by-step solution

Consult the Plot

Look at the plot of binding energy per nucleon versus the number of nucleons in the nucleus.

Locate the Elements on the Plot

On the plot, locate the positions of \(^{56}\mathrm{Fe}\) and \(^{112}\mathrm{Te}\).

Compare the Binding Energy per Nucleon

Observe the binding energy per nucleon for both elements. Note which one has a higher binding energy per nucleon.

Determine whether the Reaction is Exothermic or Endothermic

If the binding energy per nucleon of \(^{112}\mathrm{Te}\) is higher than that of \(^{56}\mathrm{Fe}\), the reaction is exothermic because it releases energy. On the other hand, if the binding energy per nucleon of \(^{112}\mathrm{Te}\) is lower than that of \(^{56}\mathrm{Fe}\), the reaction requires energy to occur and is, therefore, endothermic.

Justify the Answer

Based on the observations from the plot, justify whether the fusion of two \(^{56}\mathrm{Fe}\) atoms to produce \(^{112}\mathrm{Te}\) is an exothermic or endothermic reaction.

Key concepts

Exothermic and Endothermic Reactions

Understanding the difference between exothermic and endothermic reactions is key to grasping many concepts in chemistry, including nuclear reactions. Simply put, an exothermic reaction releases energy into its surroundings. This typically happens when the total energy of the products is less than the total energy of the reactants, indicating that energy has been released during the process. Examples of exothermic reactions include combustion and nuclear fusion in stars.

On the other hand, an endothermic reaction absorbs energy from its surroundings. In these reactions, the energy of the products is higher than the energy of the reactants, indicating that the reaction has absorbed energy to proceed. Endothermic processes are common in biochemical reactions, like photosynthesis, and in the melting of ice where heat is absorbed to change the state of water.

For the exercise regarding the fusion of uclear atoms, the determination of whether a reaction is exothermic or endothermic is based on the binding energy per nucleon. If the product nucleus has a higher binding energy per nucleon than the reactants, it would mean the reaction is exothermic, as energy is released when nucleons bind more tightly. Conversely, if the binding energy per nucleon is lower in the products, the reaction is endothermic because energy is required to achieve less stable nuclear configurations.

Nucleon Fusion Process

The nucleon fusion process is a type of nuclear reaction where two or more atomic nuclei join together to form a single heavier nucleus. During this process, a significant amount of energy can be released or absorbed, depending on the balance of nuclear binding energy before and after the reaction.

In the context of the exercise, fusing two uclear atoms involves bringing together protons and neutrons from two uclear atoms to create a uclear atom. The success and nature of this process can be influenced by factors such as the nuclear stability of the reactants and products, and the efficiency of energy release.

Role of the Curve of Binding Energy

The curve of binding energy per nucleon plays a pivotal role in understanding nuclear fusion reactions. It shows that lighter elements tend to release energy when fused—this is the principle that powers stars, including our sun. For heavier elements, the curve indicates that fusing them together would generally require energy, hence endothermic. At the peak of this curve lies iron, and any element heavier than iron, including uclear is less stable, usually making fusion processes that form elements heavier than iron endothermic.

Nuclear Chemistry

Mentioning nuclear chemistry brings to the forefront the branch of chemistry that deals with the reactions and properties of atomic nuclei. It includes the study of both stable and unstable elements, radioactive decay, fission, and fusion reactions. Nuclear chemists delve into the intricate balances of forces within the nucleus and apply this understanding to various fields such energy production, medical treatments and diagnostics, and understanding the fundamental principles of matter and energy.

In the exercise provided, we encounter an application of nuclear chemistry principles to predict the nature of a reaction between two uclear atoms. The notion of binding energy is central to nuclear chemistry, as it provides insight into the stability of nuclei and the energy changes associated with nuclear reactions.

Nuclear Stability and Binding Energy

Within nuclear chemistry, stability is a key concept; it signifies how likely a nucleus is to remain intact or change over time. The binding energy is a measure of the stability; the more energy that's required to disassemble a nucleus into its individual nucleons, the more stable it is. Thus, reactions that increase the stability of the system (going from less to more stable nuclei) tend to be exothermic. When considering the fusing of uclear atoms to form uclear, nuclear chemistry principles suggest that because iron is at the peak of stability, creating a heavier element like tellurium would require additional energy, inferring that such a reaction is likely to be endothermic.