Problem 95 - Chemistry The Science in Context

Question

The synthesis of new elements and specific isotopes of known elements in linear accelerators involves the fusion of smaller nuclei. a. An isotope of platinum can be prepared from nickel-64 and tin-124. Write a balanced equation for this nuclear reaction. (You may assume that no neutrons are ejected in the fusion reaction.) b. Substituting tin- 132 for tin- 124 increases the rate of the fusion reaction 10 times. Which isotope of \(\mathrm{Pt}\) is formed in this reaction?

Step-by-Step Solution

Answer

Question: Write a balanced nuclear reaction involving Nickel-64 and Tin-124 isotopes, and find the isotope of platinum formed when tin-124 is replaced with tin-132, knowing that the fusion reaction rate increases ten times. Answer: The balanced nuclear reaction between Nickel-64 and Tin-124 is: \(_{28}^{64}{\text{Ni}} + _{50}^{124}{\text{Sn}} \rightarrow _{78}^{188}{\text{Pt}}\) When Tin-124 is replaced with Tin-132, the isotope of platinum formed is Platinum-196: \(_{28}^{64}{\text{Ni}} + _{50}^{132}{\text{Sn}} \rightarrow _{78}^{196}{\text{Pt}}\)

Step 1: a. Balanced nuclear equation

To write a balanced nuclear reaction, we need to ensure the conservation of atomic numbers (protons) and nucleon numbers (protons + neutrons). The reaction between nickel-64 and tin-124 can be written as: \(_{28}^{64}{\text{Ni}} + _{50}^{124}{\text{Sn}} \rightarrow _{78}^{X}{\text{Pt}}\) Where X is the mass number of the platinum isotope generated. To find the mass number X, we can apply the conservation of nucleon numbers: \(X = 64 + 124 = 188\) The balanced nuclear equation is: \(_{28}^{64}{\text{Ni}} + _{50}^{124}{\text{Sn}} \rightarrow _{78}^{188}{\text{Pt}}\)

Step 2: b. Isotope of platinum formed with tin-132

The new nuclear fusion reaction will involve tin-132 instead of tin-124. To find the isotope of platinum formed in this reaction, we can apply the conservation of atomic numbers and nucleon numbers again: \(_{28}^{64}{\text{Ni}} + _{50}^{132}{\text{Sn}} \rightarrow _{78}^{Y}{\text{Pt}}\) Where Y is the mass number of the platinum isotope generated in this reaction. To find Y, we can apply the conservation of nucleon numbers: \(Y = 64 + 132 = 196\) The isotope of platinum formed in this reaction is Platinum-196: \(_{28}^{64}{\text{Ni}} + _{50}^{132}{\text{Sn}} \rightarrow _{78}^{196}{\text{Pt}}\)

Key Concepts

Isotope Synthesis

Isotope synthesis involves producing new isotopes by combining elements through nuclear reactions. In our case, we are looking at creating isotopes of platinum by using nickel and tin isotopes. The process begins with identifying the isotopes you plan to fuse. For example, nickel-64 and tin-124 can react together. This nuclear fusion results in forming an isotope of platinum. What's fascinating here is that isotopes are forms of an element with the same number of protons but different numbers of neutrons. By altering the neutron count, new isotopes are synthesized, which can have unique properties. To produce an isotope via synthesis, one must conserve the atomic and nucleon numbers during the process. This ensures that the same number of protons and "mass units" are present before and after the fusion. Thus, practicing isotope synthesis demands precise calculations and balancing of equations.

Nuclear Fusion

Nuclear fusion is the heart of many nuclear reactions and is pivotal in isotope synthesis. It involves combining two light atomic nuclei to form a heavier nucleus, releasing energy in the process. Fusion doesn't just occur haphazardly; the involved nuclei must overcome repulsive electrostatic forces to collide and merge. In the synthetic process discussed here, nickel-64 and tin isotopes undergo fusion to create platinum isotopes. Besides energy release, nuclear fusion also tells us about reaction rates. Substituting tin-124 with tin-132 increases the reaction rate significantly. This substitution makes the fusion reaction ten times faster, showcasing how changing isotopes can affect nuclear reaction dynamics significantly. Such understandings lead to optimizing conditions for isotope synthesis.

Balanced Nuclear Equations

Balanced nuclear equations are crucial in ensuring that nuclear reactions adhere to certain conservation laws. When we write a nuclear reaction, we conserve both atomic numbers (number of protons) and nucleon numbers (both protons and neutrons).In the exercise solution, balanced equations helped in determining the formation of specific platinum isotopes. For example: - To synthesize platinum-188, we performed the reaction: \(_{28}^{64}{\text{Ni}} + _{50}^{124}{\text{Sn}} \rightarrow _{78}^{188}{\text{Pt}}\)Each element in the equation contributes to the total nucleon number, ensuring a balanced equation. Similarly, replacing tin-124 with tin-132 forms platinum-196 through conservation: \(_{28}^{64}{\text{Ni}} + _{50}^{132}{\text{Sn}} \rightarrow _{78}^{196}{\text{Pt}}\)Balanced nuclear equations are a tool that scientists use to predict and verify the outcomes of nuclear reactions accurately. They ensure that reactions conserve the essential properties required by physical laws, making them reliable and practical in scientific applications.