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 \({ }^{130}\) Xe in some minerals. In what way do these two isotopes differ from one another? In what respects are they the same?

Short answer

The two isotopes, \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\), differ in their number of neutrons and atomic mass number, with 75 neutrons for \({ }^{129}\mathrm{Xe}\) and 76 neutrons for \({ }^{130}\mathrm{Xe}\). However, they are both isotopes of the element xenon (Xe) and share the same number of protons (54) and electrons (54 if the atom is neutral), leading to similar chemical properties.

Step-by-step solution

Understand isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Because they have the same number of protons, they will have the same chemical properties. However, the number of neutrons affects the atom's mass, so isotopes will have different atomic masses.

Identify the given isotopes

We are given two isotopes: \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\). Both of these isotopes are of the element xenon (Xe). In the notation for isotopes, the number above the element symbol represents the atomic mass number (number of protons + number of neutrons), while the element symbol represents the element with its unique number of protons (and electrons when the atom is neutral).

Calculate the number of protons, neutrons, and electrons for each isotope

Xenon has 54 protons and 54 electrons, as its atomic number (protons) is 54. To determine the number of neutrons, subtract the atomic number from the atomic mass number. For \({ }^{129}\mathrm{Xe}\), this would be \(129 - 54 = 75\) neutrons. For \({ }^{130}\mathrm{Xe}\), the calculation would be \(130 - 54 = 76\) neutrons.

Identify the differences between the isotopes

There is one key difference between \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\): their number of neutrons. \({ }^{129}\mathrm{Xe}\) has 75 neutrons, while \({ }^{130}\mathrm{Xe}\) has 76 neutrons. This difference also affects their atomic mass number, which is 129 and 130 respectively.

Identify the similarities between the isotopes

The two isotopes, \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\), share several properties. They are both isotopes of the element xenon (Xe), so they have the same number of protons (54) and electrons (54 if the atom is neutral). Consequently, they also have similar chemical properties since the number of protons determines the element's chemical behavior. Now we have identified both the differences and similarities between the two isotopes \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\).