Problem 128 - Chemistry: An Atoms-Focused Approach

Question

Isotopes in Geochemistry The relative abundances of the stable isotopes of the elements are not entirely constant. For example, in some geological samples (soils and rocks), the ratio of \(^{87} \mathrm{Sr}\) to \(^{86} \mathrm{Sr}\) is affected by the presence of a radioactive isotope of another element, which slowly undergoes \(\beta\) decay to produce more \(^{87} \mathrm{Sr}\). What is this other isotope?

Step-by-Step Solution

Answer

Answer: \(^{87}\mathrm{Rb}\)

Step 1: Understanding Beta Decay

In beta decay, a neutron in the nucleus is converted into a proton, and an electron (called a beta particle) is emitted. This process increases the atomic number (Z) by 1, while the mass number (A) remains unchanged.

Step 2: Analyzing the isotopes of Sr

The two isotopes we are given are \(^{87}\mathrm{Sr}\) and \(^{86}\mathrm{Sr}\). Since the ratio of these two isotopes is affected by beta decay, we need to find the radioactive isotope that undergoes beta decay to produce more \(^{87}\mathrm{Sr}\). The mass number of the product isotope should be the same as \(^{87}\mathrm{Sr}\), that is, A = 87. However, since beta decay increases the atomic number by 1, we need to find an isotope with an atomic number one less than Sr.

Step 3: Identifying the element with the required atomic number

Strontium (Sr) has an atomic number of 38. Therefore, we are looking for an element with an atomic number of 37. That element is Rb (Rubidium).

Step 4: Identifying the radioactive isotope of Rb that decays to produce \(^{87}\mathrm{Sr}\)

As we determined earlier, the mass number (A) should be the same, that is 87. So, we are looking for an isotope of Rubidium with a mass number of 87. That isotope is \(^{87}\mathrm{Rb}\). Therefore, the radioactive isotope that undergoes beta decay to produce more \(^{87}\mathrm{Sr}\) is \(^{87}\mathrm{Rb}\).

Key Concepts

Geochemistry

Geochemistry is the scientific study of the Earth's chemical composition and processes. It's about understanding the elements and isotopes that are present in rocks, minerals, and soils. This field helps scientists unravel the Earth's history and the processes that shape our planet. Isotopes play a crucial role in geochemistry, providing insights into ages and origins of rocks and minerals.

• Isotopes are variants of the same element but with different mass numbers due to varying numbers of neutrons.
• Stable isotopes do not decay over time, while radioactive isotopes decay at a predictable rate.
• The study of isotope ratios helps in tracing the processes and conditions of Earth's formation and evolution.

In geochemistry, radioactive decay of isotopes changes these ratios, providing important information about geological materials.

Beta Decay

Beta decay is a type of radioactive decay where a neutron in an unstable nucleus is transformed into a proton. This transformation also emits a beta particle, which is essentially a high-energy electron or positron.

• During beta decay, the atomic number of an element increases by one, since a neutron becomes a proton.
• The mass number, however, remains unchanged because protons and neutrons have similar masses.
• Beta decay is responsible for converting one type of element into another, which affects the elemental composition over time.

This process is particularly significant in geochemistry as it alters the isotopic ratios, making it a valuable tool for radiometric dating and understanding Earth's history.

Isotope Ratios

The ratio of isotopes in a sample provides key insights into the sample's history and formation processes. Isotope ratios are essential in fields such as geology, anthropology, and environmental science. By analyzing the ratios, scientists can draw conclusions about past climates, geological processes, and even trace biological pathways.

• Each isotope has a characteristic half-life through which it decays at a constant rate.
• This constancy allows scientists to use isotope ratios as a "clock" to date materials, a technique known as radiometric dating.
• The ratio of isotopes such as \(^{87} \mathrm{Sr}/^{86} \mathrm{Sr}\) can change through processes like beta decay, offering clues to geological events.

In summary, isotopic analysis is a window into understanding the timing and mechanics of natural processes.

Radioactive Decay

Radioactive decay is a spontaneous process in which unstable atomic nuclei lose energy by emitting radiation. This phenomenon alters the atomic and/or mass number of the isotope, creating a different element or isotope in the process.

• There are several types of radioactive decay: alpha decay, beta decay, and gamma decay, each involving different particles and energy emissions.
• radioactive decay is predictable and quantifiable; isotopes decay at a constant rate known as the half-life.
• In geochemistry, the gradual transformation of one isotope to another provides a means to date geological samples through radiometric dating.

Understanding radioactive decay is fundamental for interpreting the age, development, and transformation processes within geological materials.