Isotope Practice Worksheet With Answers

Isotope Practice Worksheet: Mastering Isotopes with Solved Examples

Understanding isotopes is crucial for grasping fundamental concepts in chemistry and physics. This comprehensive worksheet will guide you through various isotope-related problems, providing explanations and solutions to solidify your understanding. We'll cover calculating atomic mass, identifying isotopes, and working with isotopic abundance. By the end, you'll be confident in tackling any isotope-related question.

Introduction to Isotopes

Atoms of the same element always have the same number of protons, defining their atomic number. However, they can have different numbers of neutrons. These variations are called isotopes. Isotopes of an element have the same atomic number but different mass numbers (the sum of protons and neutrons). For example, carbon-12 (¹²C) and carbon-14 (¹⁴C) are isotopes of carbon. Both have 6 protons, but ¹²C has 6 neutrons, while ¹⁴C has 8 neutrons. This difference in neutron number affects the atomic mass but not the chemical properties significantly.

Understanding Isotopic Notation

Isotopes are typically represented using isotopic notation: ^A_Z X, where:

• A represents the mass number (protons + neutrons).
• Z represents the atomic number (number of protons).
• X is the element symbol.

For example, ¹⁴₆C denotes a carbon isotope with a mass number of 14 and an atomic number of 6. This means it has 6 protons and 8 neutrons (14 - 6 = 8).

Calculating Atomic Mass

The atomic mass of an element is the weighted average of the masses of its isotopes, considering their relative abundance. This is often expressed in atomic mass units (amu). The formula for calculating atomic mass is:

Atomic Mass = Σ [(Isotope Mass) x (Isotopic Abundance)]

Where:

• Isotope Mass is the mass of a specific isotope.
• Isotopic Abundance is the percentage abundance of that isotope (expressed as a decimal).
• Σ represents the sum of all isotopes.

Practice Problems: Calculating Atomic Mass

Let's work through some examples:

Problem 1:

Chlorine has two naturally occurring isotopes: ³⁵Cl (34.97 amu, 75.77% abundance) and ³⁷Cl (36.97 amu, 24.23% abundance). Calculate the average atomic mass of chlorine.

Solution:

Atomic Mass = [(34.97 amu) x (0.7577)] + [(36.97 amu) x (0.2423)] = 26.49 amu + 8.95 amu = 35.44 amu

Problem 2:

Boron exists as two isotopes: ¹⁰B (10.01 amu) and ¹¹B (11.01 amu). The average atomic mass of boron is 10.81 amu. Determine the percent abundance of each isotope.

Solution:

Let x be the abundance of ¹⁰B (as a decimal). Then (1-x) is the abundance of ¹¹B.

10.81 amu = (10.01 amu)(x) + (11.01 amu)(1-x) 10.81 = 10.01x + 11.01 - 11.01x 0.80 = x x = 0.80 or 80%

Therefore:

• Abundance of ¹⁰B = 80%
• Abundance of ¹¹B = 100% - 80% = 20%

Problem 3:

Magnesium has three isotopes: ²⁴Mg, ²⁵Mg, and ²⁶Mg. The average atomic mass of Magnesium is 24.31 amu. The abundance of ²⁴Mg is 78.99% and ²⁶Mg is 11.01%. Calculate the abundance of ²⁵Mg and the masses of ²⁵Mg and ²⁶Mg, assuming the mass of ²⁴Mg is 23.99 amu.

Solution:

This problem requires a bit more algebra. Let's denote the abundance of ²⁵Mg as 'y' and the mass of ²⁵Mg as 'm1' and the mass of ²⁶Mg as 'm2'.

24.31 = (23.99)(0.7899) + (m1)(y) + (m2)(0.1101)

Since the abundance must add up to 100%, we know: y = 1 - 0.7899 - 0.1101 = 0.1

Now we have a single equation with two unknowns. This problem is unsolvable without further information. We need either the mass of ²⁵Mg or ²⁶Mg, or the average mass of ²⁵Mg and ²⁶Mg to solve for both simultaneously. This highlights the importance of complete data in isotopic calculations.

Identifying Isotopes

This section focuses on identifying isotopes based on their proton and neutron counts.

Problem 4:

An atom has 17 protons and 20 neutrons. Identify the element and its isotopic notation.

Solution:

An atom with 17 protons is chlorine (Cl). The mass number is 17 + 20 = 37. Therefore, the isotopic notation is ³⁷₁₇Cl.

Problem 5:

Two isotopes have the following characteristics: Isotope A: 12 protons, 12 neutrons. Isotope B: 12 protons, 13 neutrons. Identify the element and write the isotopic notation for both isotopes. Are these isotopes radioactive?

Solution:

Both Isotopes have 12 protons, identifying the element as Magnesium (Mg).

• Isotope A: ¹²₁₂Mg
• Isotope B: ¹³₁₂Mg

Whether these isotopes are radioactive depends on their stability. ¹²Mg is a stable isotope, while ¹³Mg is radioactive with a very short half-life. Note that stability is not always easily predictable and often needs to be looked up in reference material.

Isotopic Abundance and Natural Samples

The abundance of isotopes varies in nature. This variation is vital in various applications, including radiometric dating and tracing the movement of elements.

Problem 6:

A sample of lithium contains 92.5% ⁷Li and 7.5% ⁶Li. The atomic mass of ⁷Li is 7.016 amu and the atomic mass of ⁶Li is 6.015 amu. Calculate the average atomic mass of lithium in this sample.

Solution:

Average Atomic Mass = (7.016 amu)(0.925) + (6.015 amu)(0.075) = 6.941 amu

Frequently Asked Questions (FAQ)

Q1: What is the difference between atomic number and mass number?

The atomic number is the number of protons in an atom's nucleus, defining the element. The mass number is the sum of protons and neutrons in the nucleus.

Q2: Are all isotopes radioactive?

No. Many isotopes are stable, meaning they do not undergo radioactive decay. However, some isotopes are unstable and undergo radioactive decay, emitting particles or energy to become more stable.

Q3: How are isotopes used in real-world applications?

Isotopes have numerous applications, including:

• Radioactive dating: Determining the age of artifacts and geological formations.
• Medical imaging and treatment: Radioactive isotopes are used in PET scans and radiotherapy.
• Industrial tracers: Tracking the movement of materials in industrial processes.
• Scientific research: Studying chemical reactions and biological processes.

Q4: Can isotopic abundance change?

While the overall abundance of isotopes in nature is relatively constant for a given element, minor variations can occur depending on the source material. This is especially relevant in situations involving geological processes or human intervention.

Conclusion

This worksheet provides a solid foundation for understanding isotopes and their applications. Remember, mastering isotopes requires practice and a good grasp of basic atomic structure. By working through these problems and understanding the underlying concepts, you'll build a stronger understanding of chemistry and physics. Don't hesitate to review the concepts and practice further using additional problems from your textbook or online resources. The key to success is consistent practice and attention to detail!