Equal Amounts of Each Sample

Oct 13, 2025 by vinooalluri.com 72 views

Radioactive decay is a fundamental concept in chemistry, where unstable atoms lose energy and stability by emitting radiation. In this article, we will explore the half-life of four different isotopes of sulfur and determine which jar will contain the least amount of the isotope after 10 half-lives.

The Half-Life of Sulfur Isotopes

The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay. The table below lists the half-life of four different isotopes of sulfur:

Isotope	Half-Life (years)
³⁴S	0.87 seconds
³⁵S	87.2 seconds
³⁶S	2.88 x 10^5 years
³⁷S	1.36 x 10^6 years

Equal Amounts of Each Sample

Let's assume that equal amounts of each sample are stored in sealed jars. This means that each jar initially contains the same amount of the isotope.

Radioactive Decay: A 10-Half-Life Analysis

We want to determine which jar will contain the least amount of the isotope after 10 half-lives. To do this, we need to calculate the remaining amount of each isotope after 10 half-lives.

³⁴S: The Shortest Half-Life

The half-life of ³⁴S is 0.87 seconds. After 10 half-lives, the remaining amount of ³⁴S will be:

(1/2)^10 = 1/1024 ≈ 0.0009765625

This means that after 10 half-lives, the jar containing ³⁴S will have approximately 0.0009765625% of the initial amount.

³⁵S: A Moderate Half-Life

The half-life of ³⁵S is 87.2 seconds. After 10 half-lives, the remaining amount of ³⁵S will be:

(1/2)^10 = 1/1024 ≈ 0.0009765625

This means that after 10 half-lives, the jar containing ³⁵S will have approximately 0.0009765625% of the initial amount.

³⁶S: A Long Half-Life

The half-life of ³⁶S is 2.88 x 10^5 years. After 10 half-lives, the remaining amount of ³⁶S will be:

(1/2)^10 = 1/1024 ≈ 0.0009765625

This means that after 10 half-lives, the jar containing ³⁶S will have approximately 0.0009765625% of the initial amount.

³⁷S: The Longest Half-Life

The half-life of ³⁷S is 1.36 x 10^6 years. After 10 half-lives, the remaining amount of ³⁷S will be:

(1/2)^10 = 1/1024 ≈ 0.0009765625

This means that after 10 half-lives, the jar containing ³⁷S will have approximately 0.0009765625% of the initial amount.

Conclusion

After analyzing the half-life of each isotope, we can conclude that all four jars will contain approximately 0.0009765625% of the initial amount after 10 half-lives. However, since the question asks which jar will contain the least amount of the isotope, we need to consider the initial amount of each isotope.

The Correct Answer

Since the half-life of ³⁴S is the shortest, it will decay the fastest. Therefore, the jar containing ³⁴S will contain the least amount of the isotope after 10 half-lives.

Final Thoughts

In our previous article, we explored the half-life of four different isotopes of sulfur and determined which jar will contain the least amount of the isotope after 10 half-lives. In this article, we will answer some frequently asked questions related to radioactive decay and sulfur isotopes.

Q: What is radioactive decay?

A: Radioactive decay is a process in which unstable atoms lose energy and stability by emitting radiation. This process occurs when an atom has too many or too few neutrons, causing it to become unstable and decay into a more stable form.

Q: What is the half-life of a radioactive isotope?

A: The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay. This is a fundamental concept in chemistry and is used to predict the rate of decay and the remaining amount of the isotope after a certain period.

Q: Why do different isotopes have different half-lives?

A: Different isotopes have different half-lives because they have different numbers of neutrons and protons in their atomic nuclei. This affects the stability of the atom and the rate at which it decays.

Q: Can radioactive decay be stopped?

A: No, radioactive decay cannot be stopped. Once an atom has begun to decay, it will continue to do so until it reaches a stable form. However, the rate of decay can be slowed down or accelerated by changing the conditions under which the atom is stored.

Q: How do scientists measure the half-life of a radioactive isotope?

A: Scientists measure the half-life of a radioactive isotope by counting the number of decays that occur over a period of time. This is typically done using a device called a Geiger counter, which detects the radiation emitted by the decaying atoms.

Q: What are some common applications of radioactive decay?

A: Radioactive decay has many practical applications, including:

Medical imaging: Radioactive isotopes are used to create images of the body and diagnose diseases such as cancer.
Cancer treatment: Radioactive isotopes are used to kill cancer cells and slow down the growth of tumors.
Food irradiation: Radioactive isotopes are used to kill bacteria and other microorganisms that can cause foodborne illness.
Industrial applications: Radioactive isotopes are used to detect leaks and measure the thickness of materials.

Q: Are all radioactive isotopes equally hazardous?

A: No, not all radioactive isotopes are equally hazardous. Some isotopes, such as ³⁴S, have very short half-lives and are relatively harmless, while others, such as ²³⁸U, have very long half-lives and can be highly hazardous.

Q: How can I protect myself from radioactive decay?

A: To protect yourself from radioactive decay, you should:

Avoid exposure to radioactive materials: If you work with radioactive materials, make sure to follow proper safety protocols and wear protective gear.
Use shielding: If you are working with radioactive materials, use shielding to block the radiation.
Follow proper disposal procedures: If you are disposing of radioactive materials, make sure to follow proper procedures to prevent contamination.

Conclusion

Radioactive decay is a complex process that involves the loss of energy and stability by unstable atoms. Understanding the half-life of different isotopes is crucial in chemistry, as it helps us predict the rate of decay and the remaining amount of the isotope after a certain period. In this article, we answered some frequently asked questions related to radioactive decay and sulfur isotopes.