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 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?

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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

Step 4: 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.

Step 5: 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.

Key Concepts

Xenon Isotopes

Xenon, represented by the chemical symbol Xe, is a noble gas. Noble gases are known for their stability and lack of chemical reactivity under standard conditions. Xenon itself is colorless, dense, and found in Earth’s atmosphere at low concentrations. One fascinating aspect of xenon is its isotopes. An isotope of an element is an atom that has the same number of protons, defining the chemical properties, but a different number of neutrons. This leads to a variety of "versions" of xenon that differ in mass. The isotopes of xenon, such as those mentioned -

• ¹²⁹Xe with a mass number of 129
• ¹³⁰Xe with a mass number of 130

- have identical chemical responses due to having the same number of protons (54), but vary physically due to the differences in neutrons. Isotopes can be stable or radioactive. Stable isotopes, like these, do not decay over time, while radioactive ones lose particles, changing into different elements or isotopes over time. The study of xenon's isotopic ratios in Earth's crust helps scientists learn more about geological and planetary processes. Understanding xenon and its isotopes provides valuable insight into the natural world. It is crucial to recognize that isotopes, while differing in mass, remain the same element since they share the same atomic structure aside from neutrons.

Neutrons in Isotopes

Neutrons are subatomic particles found in the nucleus of an atom. They carry no electrical charge, unlike protons which are positively charged, and electrons which are negatively charged. Thus, neutrons act as neutral particles that add mass without affecting the electrical balance of the atom. The presence of neutrons is a key factor in the formation of isotopes. While the number of protons (the atomic number) stays constant within a particular element, the number of neutrons can vary, resulting in different isotopes. In the case of xenon isotopes:

• ¹²⁹Xe has 75 neutrons (129 - 54 = 75)
• ¹³⁰Xe has 76 neutrons (130 - 54 = 76)

This difference in neutron count contributes to the variation in mass number, illustrating how isotopes of the same element can have unique physical properties yet remain chemically identical. Neutrons play a significant role in nuclear stability. The varying neutron-to-proton ratios in isotopes influence the stability and natural abundance of these isotopes, making the understanding of neutrons vital for fields like nuclear chemistry, physics, and environmental studies.

Understanding Mass Number

Mass number is an important concept when discussing isotopes. It refers to the total number of protons and neutrons in an atom’s nucleus. In terms of notation, the mass number is typically written as a superscript preceding the element symbol. For example, in ¹²⁹Xe, 129 is the mass number. The mass number associates closely with isotopes, as it varies based on the number of neutrons in the nucleus while the proton count remains the same. This causes isotopes of a single element to differ in mass but not in chemical types. Mass number calculation is simple:

• Mass number = number of protons + number of neutrons

Why is the mass number significant? Determining the mass number of different isotopes allows for understanding of their relative masses and stability. It provides clues into phenomena such as the stability of atomic nuclei and how different isotopes behave under various physical conditions. By studying mass numbers, scientists can illuminate patterns in elemental and isotopic behavior, as well as in the mechanisms behind nuclear reactions and elemental formation in the universe. It's a key tool in the realm of nuclear science.