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Chapter 2: Problem 32

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 1129 \(\mathrm{Xe}\) 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?

Short Answer

Expert verified
The isotopes \(^{129}\mathrm{Xe}\) and \(^{130}\mathrm{Xe}\) are both isotopes of the element Xenon, with the same atomic number of 54, meaning they have the same number of protons and exhibit the same chemical behavior. However, they differ in their number of neutrons and mass numbers, with \(^{129}\mathrm{Xe}\) having 75 neutrons and a mass number of 129, while \(^{130}\mathrm{Xe}\) has 76 neutrons and a mass number of 130.

Step by step solution

01

Understand isotopes

Isotopes are atoms of the same element with different numbers of neutrons in their nucleus. The number of protons in an atom determines the element it belongs to, while the number of neutrons can vary. The total number of protons and neutrons in an atom is called its mass number, so isotopes of an element will have different mass numbers.
02

Identify the isotopes

In this exercise, we are given two isotopes: \(^{129}\mathrm{Xe}\) and \(^{130}\mathrm{Xe}\). The superscript number in front of the element symbol indicates the mass number of the isotope. In this case, both isotopes are of the element Xenon (Xe). The atomic number of Xenon is 54, which means that it has 54 protons in its nucleus.
03

Determine the number of neutrons

To find the number of neutrons in each isotope, we can subtract the atomic number (number of protons) from the mass number. For \(^{129}\mathrm{Xe}\): \(129 - 54 = 75\) neutrons For \(^{130}\mathrm{Xe}\): \(130 - 54 = 76\) neutrons
04

Explain the differences

The two isotopes, \(^{129}\mathrm{Xe}\) and \(^{130}\mathrm{Xe}\), differ from one another in terms of the number of neutrons present in their nucleus. \(^{129}\mathrm{Xe}\) has 75 neutrons while \(^{130}\mathrm{Xe}\) has 76 neutrons. This difference in the number of neutrons results in different mass numbers for the two isotopes.
05

Explain the similarities

In terms of similarities, both isotopes are of the same element, Xenon. They share the same atomic number, which is 54, meaning they have the same number of protons in their nucleus. Since the number of protons determines the element's chemical properties, both isotopes will exhibit the same chemical behavior.

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