Problem 32 - Chemistry: The Central Science

Question

One way in which Earth's evolution as a planet can be understood is by measuring the amounts of certain isotopes in rocks. One quantity recently measured is the ratio of \({ }^{129} \mathrm{Xe}\) to \({ }^{130} \mathrm{Xe}\) in some minerals. In what way do these two isotopes differ from one another? In what respects are they the same?

Step-by-Step Solution

Answer

The isotopes \({ }^{129} \mathrm{Xe}\) and \({ }^{130} \mathrm{Xe}\) differ in their number of neutrons (75 and 76, respectively) and mass numbers (129 and 130, respectively). However, they are the same in terms of their atomic number (54), number of protons (54), and number of electrons (54), resulting in identical chemical properties.

Step 1: Understanding Isotopes

Isotopes are atoms of the same element that have the same number of protons, but a different number of neutrons in their nucleus. As a result, isotopes have the same atomic number (Z, which determines the element), but a different mass number (A, which is the sum of the number of protons and neutrons). The isotopes can be represented as \({ }^{A} \mathrm{Element}\) (mass number on the superscript, and the element symbol).

Step 2: Identifying Atomic Structure of Xenon Isotopes

Now, our goal is to identify the atomic structure of the two given isotopes, \({ }^{129} \mathrm{Xe}\) and \({ }^{130} \mathrm{Xe}\). Xenon (Xe) is a chemical element with the atomic number Z = 54. We can now determine the number of protons (P), electrons (E), and neutrons (N) in these isotopes. For \({ }^{129} \mathrm{Xe}\): - P = Z = 54 (same for all isotopes of Xenon) - E = P = 54 (as the isotopes are electrically neutral) - N = A - Z = 129 - 54 = 75 For \({ }^{130} \mathrm{Xe}\): - P = Z = 54 (same for all isotopes of Xenon) - E = P = 54 (as the isotopes are electrically neutral) - N = A - Z = 130 - 54 = 76

Step 3: Differences between \({ }^{129} \mathrm{Xe}\) and \({ }^{130} \mathrm{Xe}\)

The difference between the two isotopes lies in the number of neutrons. \({ }^{129} \mathrm{Xe}\) has 75 neutrons, while \({ }^{130} \mathrm{Xe}\) has 76 neutrons. As a result, their mass numbers (A) are also different: 129 for \({ }^{129} \mathrm{Xe}\) and 130 for \({ }^{130} \mathrm{Xe}\).

Step 4: Similarities between \({ }^{129} \mathrm{Xe}\) and \({ }^{130} \mathrm{Xe}\)

The similarities between the two isotopes are: 1. Both are isotopes of Xenon, and they have the same atomic number (54). This means that they have the same number of protons. 2. Both isotopes have the same number of electrons (54) as they have protons since they are electrically neutral atoms. This results in identical chemical properties, as it is the electrons involved in chemical reactions. In conclusion, the isotopes \({ }^{129} \mathrm{Xe}\) and \({ }^{130} \mathrm{Xe}\) differ in their number of neutrons and mass numbers, while they are the same in terms of their atomic number, number of protons, and number of electrons, as well as their chemical properties.