Isotopes: Videos & Practice Problems

Isotopes are atoms of the same element that differ in the number of neutrons, leading to varying mass numbers while maintaining the same atomic number. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14, with mass numbers of 12, 13, and 14, respectively. Radioactive isotopes, like carbon-14, are unstable and decay over time, emitting energy and particles. Their decay rate is measured by half-life, crucial for applications in medicine and radiometric dating of fossils, highlighting their significance in both scientific research and practical uses.

Isotopes

Atoms are the fundamental building blocks of matter, and while all atoms of a given element share the same number of protons, they can differ in the number of neutrons. This variation leads to the formation of isotopes, which are defined as atoms of the same element that have the same atomic number (number of protons) but different mass numbers due to differing numbers of neutrons.

The mass number of an atom is calculated by summing the total number of protons and neutrons in its nucleus. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14. All three isotopes have 6 protons, which is the atomic number of carbon. However, they differ in their neutron counts: carbon-12 has 6 neutrons, carbon-13 has 7 neutrons, and carbon-14 has 8 neutrons. Consequently, their mass numbers are 12, 13, and 14, respectively.

To calculate the mass number for each isotope, the formula is:

Mass Number = Number of Protons + Number of Neutrons

For carbon-12: 6 protons + 6 neutrons = 12

For carbon-13: 6 protons + 7 neutrons = 13

For carbon-14: 6 protons + 8 neutrons = 14

While isotopes of an element have the same number of protons and electrons, they can differ in abundance. For instance, carbon-12 is the most abundant isotope, making up about 99% of all carbon atoms, while carbon-13 and carbon-14 are much less common. This abundance affects the atomic mass of the element, which is the weighted average of all isotopes. For carbon, the atomic mass is approximately 12.011, reflecting the predominance of carbon-12 and the minor contributions from the heavier isotopes.

Understanding isotopes is crucial in various fields, including chemistry, physics, and environmental science, as they play significant roles in processes such as radioactive decay and radiometric dating.

What is TRUE about carbon-13 and carbon-14?
a) They are isotopes.
b) They have the same mass number.
c) They have the same number of neutrons in their nuclei.
d) They behave differently in biological reactions.
e) None of the above are true.

• A. They are isotopes.
• B. They have the same mass number.
• C. They have the same number of neutrons in their nuclei.
• D. They behave differently in biological reactions.
• E. None of the above are true.

Answer: (A)

How are Carbon-13 and Nitrogen-15 respectively different from the more abundant isotopes Carbon-12 and Nitrogen-14?  Carbon-13 and Nitrogen-15 _______________:
a) Each have an extra neutron.     
b) Each have an extra proton.     
c) Each have one less neutron.
d) Each have one less proton.      
e) Each have one less electron.  

• A. Each have an extra neutron.
• B. Each have an extra proton.
• C. Each have one less neutron.
• D. Each have one less proton.
• E. Each have one less electron.

Answer: (A)

The atomic number of nitrogen is 7. Nitrogen-15 has a greater mass number than nitrogen-14 because the atomic nucleus of nitrogen-15 contains ________.
a) 7 neutrons.
b) 8 neutrons.
c) 8 protons.
d) 15 protons.

• A. 7 neutrons.
• B. 8 neutrons.
• C. 8 protons.
• D. 15 protons.

Answer: (B)

Radioactive Isotopes

Radioactive isotopes are a specific type of isotope characterized by their instability, leading them to decay over time while emitting energy in the form of rays or particles. A prime example is Carbon-14, which consists of 6 protons and 8 neutrons, giving it a mass number of 14. The decay process of Carbon-14 involves the release of energy and subatomic particles, indicating its radioactive nature.

The rate at which these isotopes decay is consistent, allowing scientists to determine a key concept known as the half-life. The half-life is defined as the time required for half of the radioactive atoms in a sample to decay. This predictable decay rate is crucial for various applications, particularly in medicine and geology.

In medicine, radioactive isotopes play a vital role in diagnostic imaging techniques, such as MRIs, and other therapeutic applications. Additionally, they are instrumental in radiometric dating, a method used by scientists to estimate the age of fossils, including dinosaur bones. By measuring the remaining amount of radioactive isotopes and applying the concept of half-life, researchers can approximate the age of these ancient specimens.

Understanding the properties and applications of radioactive isotopes is essential, as they not only contribute to advancements in medical technology but also enhance our knowledge of geological time scales through dating techniques.

Radioactive isotopes are utilized for all of the following except:
a) Dating fossilized material of once living things.
b) Radiation treatment to slow or stop the development of cancer cells.
c) Labeling regions of the body with radioactivity for special imaging techniques.
d) All of the above.

• A. Dating fossilized material of once living things.
• B. Radiation treatment to slow or stop the development of cancer cells.
• C. Labeling regions of the body with radioactivity for special imaging techniques.
• D. All of the above.

Answer: (D)

The isotope Carbon-14 has a half-life of 5,730 years. How many years must pass for a sample of Carbon-14 to break down to ¼ of its original amount?
a) 5,730 years 
b) 17,190
c) 11,460
d) 2,865

• A. 5,730 years
• B. 17,190
• C. 11,460
• D. 2,865

Answer: (C)

Here’s what students ask on this topic:

What are isotopes and how do they differ from each other?

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This difference in neutron count leads to varying mass numbers among isotopes. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14, with mass numbers of 12, 13, and 14, respectively. Despite these differences in mass number, all isotopes of an element share the same atomic number, which is the number of protons. This is because changing the number of protons would change the element itself. The varying number of neutrons in isotopes results in different physical properties, such as stability and atomic mass.

What is the significance of radioactive isotopes in scientific research and practical applications?

Radioactive isotopes are significant in both scientific research and practical applications due to their instability and ability to decay over time, emitting energy and particles. This decay process is measured by the half-life, which is the time it takes for half of the radioactive atoms in a sample to break down. In medicine, radioactive isotopes are used in diagnostic imaging techniques like MRIs and in treatments for certain diseases. In geology and archaeology, they are used for radiometric dating, which helps determine the age of fossils and rocks by measuring the remaining radioactive isotopes and calculating their half-lives. This makes radioactive isotopes invaluable tools in various fields.

How is the atomic mass of an element calculated considering its isotopes?

The atomic mass of an element is calculated as the weighted average of the masses of all its isotopes, taking into account their relative abundances. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14. Carbon-12 is the most abundant, making up about 99% of all carbon atoms. The atomic mass is close to the mass number of the most abundant isotope but slightly adjusted to account for the presence of the other isotopes. The formula for calculating atomic mass is:

$\mathrm{Atomic} \mathrm{mass}=\sum _{i=1}^n(\mathrm{fractional} \mathrm{abundance} \mathrm{of} \mathrm{isotope} i) \times \mathrm{mass} \mathrm{of} \mathrm{isotope} i$

What is a half-life and how is it used in radiometric dating?

A half-life is the time required for half of the radioactive atoms in a sample to decay. This consistent rate of decay allows scientists to use half-lives to date materials, a process known as radiometric dating. By measuring the remaining amount of a radioactive isotope in a sample and knowing its half-life, scientists can calculate the age of the sample. For example, carbon-14, with a half-life of about 5,730 years, is commonly used to date organic materials like fossils. The formula for calculating the age of a sample using half-life is:

$\mathrm{Age}=\mathrm{half-life} \times (\log (\mathrm{initial} \mathrm{amount}/\mathrm{remaining} \mathrm{amount})/\log (2\left)\right)$

How do isotopes affect the atomic mass of an element?

Isotopes affect the atomic mass of an element by contributing to the weighted average of the masses of all the isotopes of that element. Since isotopes have different numbers of neutrons, they have different mass numbers. The atomic mass is calculated by averaging these mass numbers, weighted by their relative abundances. For example, carbon's atomic mass is approximately 12.011 because carbon-12 is the most abundant isotope, making up about 99% of all carbon atoms, while carbon-13 and carbon-14 are much less abundant. This weighted average ensures that the atomic mass reflects the natural distribution of an element's isotopes.