Practice Isotope Calculations #2 – Answer Key

Have you ever wondered how scientists can determine the age of ancient artifacts or trace the movement of pollutants through the environment? The answer lies in the fascinating world of isotopes, atoms of the same element that vary in their neutron count. Understanding isotope calculations is essential for many scientific disciplines, from archaeology to geology to environmental science.

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This article serves as your comprehensive answer key to the practice isotope calculations #2 worksheet, providing detailed explanations and solutions for each problem. Whether you’re a student studying chemistry or a professional working in a related field, this guide will help you solidify your understanding of isotope calculations and their applications. Let’s dive in and unlock the secrets hidden within the world of atoms!

Understanding Isotope Fundamentals

Before tackling the practice problems, let’s review the fundamental concepts of isotopes:

• Atomic Number: The number of protons in an atom’s nucleus, defining the element’s identity.
• Mass Number: The total number of protons and neutrons in an atom’s nucleus.
• Isotopes: Atoms of the same element with the same atomic number but different mass numbers due to varying neutron counts.
• Isotopic Abundance: The relative percentage of each isotope naturally occurring in a sample.
• Radioactive Isotopes: Isotopes with an unstable nucleus that undergoes radioactive decay, transforming into a different element or isotope.

Practice Problems: Answer Key

Problem 1: Calculating Average Atomic Mass

Question: Calculate the average atomic mass of chlorine (Cl) given the following isotopic abundances: ³⁵Cl (75.77%) and ³⁷Cl (24.23%).

Solution:

Average Atomic Mass = (Isotopic Abundance of ³⁵Cl * Mass of ³⁵Cl) + (Isotopic Abundance of ³⁷Cl * Mass of ³⁷Cl)

Average Atomic Mass = (0.7577 * 35 amu) + (0.2423 * 37 amu) = 35.45 amu

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Problem 2: Determining Isotopic Abundance

Question: An element has two isotopes with mass numbers 63 and 65. The average atomic mass is 63.55 amu. Calculate the isotopic abundance of each isotope.

Solution:

Let x be the abundance of isotope 63 and (1-x) be the abundance of isotope 65.

Average Atomic Mass = (x * mass of isotope 63) + ((1-x) * mass of isotope 65)

63.55 = (x * 63) + ((1-x) * 65)

Solving for x, we get x = 0.725 or 72.5%

Therefore, the abundance of isotope 63 is 72.5% and the abundance of isotope 65 is (1-0.725) = 27.5%.

Problem 3: Radioactive Decay

Question: The half-life of carbon-14 (¹⁴C) is 5,730 years. If a sample of wood contains 1/8th the amount of ¹⁴C found in living trees, how old is the sample?

Solution:

After one half-life, the amount of ¹⁴C reduces to half.

After two half-lives, the amount of ¹⁴C reduces to one-quarter of the original amount.

After three half-lives, the amount of ¹⁴C reduces to one-eighth of the original amount.

Therefore, the wood sample is three half-lives old, which corresponds to 3 * 5,730 years = 17,190 years.

Problem 4: Calculating Isotopic Ratios

Question: A geological sample contains 10,000 atoms of oxygen-16 (¹⁶O) and 100 atoms of oxygen-18 (¹⁸O). Calculate the ¹⁸O/¹⁶O isotopic ratio.

Solution:

Isotopic Ratio (¹⁸O/¹⁶O) = (Number of ¹⁸O atoms) / (Number of ¹⁶O atoms)

Isotopic Ratio = 100 atoms / 10,000 atoms = 0.01

Why Studying Isotopes Matters

Understanding isotope calculations is essential for various scientific disciplines:

• Archaeology: Radiocarbon dating using ¹⁴C helps determine the age of ancient artifacts and remains, shedding light on human history and prehistory.
• Geology: Isotope ratios of elements like uranium and lead are used to estimate the age of rocks and minerals, providing insights into Earth’s geological history.
• Environmental Science: Isotopes are used to track the movement of pollutants, such as heavy metals, in the environment and assess their impact on ecosystems.
• Medicine: Radioactive isotopes are used in medical imaging techniques, such as PET scans, to diagnose and monitor diseases.

Beyond the Basics: Advanced Isotope Applications

The applications of isotopes extend beyond the basic calculations explored in this article. Here are some key areas where advanced isotope techniques are revolutionizing scientific research:

• Paleoclimate Studies: Isotopes in ice cores and sediment layers provide valuable information about past climate conditions, helping scientists understand climate change over time.
• Forensic Science: Isotopes in hair, bone, and other samples can be used to determine a person’s geographical origin or travel history, assisting in criminal investigations.
• Cosmology: Isotope ratios in meteorites and other celestial bodies provide insights into the formation and evolution of the universe.

Practice Isotope Calculations #2 Answer Key

Conclusion

Mastering isotope calculations is a key step towards understanding various scientific disciplines and unlocking the secrets hidden within the atom. This article has provided you with a comprehensive answer key to practice isotope calculations #2, equipping you with the knowledge and skills to tackle more complex problems. As you continue your exploration of isotopes, remember that these tiny particles hold immense power to reveal the wonders of our world.