Equation to Represent the Problem

Oct 13, 2025 by wbrum.org 133 views

Introduction

Arsenic-74 is a radioactive isotope used in medical imaging to locate brain tumors. Its half-life of 17.5 days makes it an ideal candidate for this purpose. In this article, we will explore the decay factor of Arsenic-74, write an equation to represent its decay, and calculate the amount remaining after 6 days from a 90-mg sample.

Decay Factor

The decay factor is a measure of the rate at which a radioactive substance decays. It is calculated using the formula:

Decay factor = 2^(t/T)

where t is the time elapsed and T is the half-life of the substance.

In this case, the half-life of Arsenic-74 is 17.5 days. To calculate the decay factor after 6 days, we can plug in the values:

Decay factor = 2^(6/17.5) Decay factor ≈ 0.928

Equation to Represent the Problem

The decay of a radioactive substance can be represented by the equation:

A(t) = A0 * (1/2)^(t/T)

where A(t) is the amount remaining at time t, A0 is the initial amount, t is the time elapsed, and T is the half-life of the substance.

In this case, the initial amount is 90 mg, the time elapsed is 6 days, and the half-life is 17.5 days. Plugging in these values, we get:

A(6) = 90 * (1/2)^(6/17.5)

Calculating the Amount Remaining

To calculate the amount remaining after 6 days, we can use the equation above:

A(6) = 90 * (1/2)^(6/17.5) A(6) ≈ 90 * 0.928 A(6) ≈ 83.52 mg

Therefore, after 6 days, approximately 83.52 mg of Arsenic-74 will remain from a 90-mg sample.

Discussion

The length of a half-life is a measure of the stability of a radioactive substance. A shorter half-life indicates a more unstable substance, while a longer half-life indicates a more stable substance. In this case, the half-life of Arsenic-74 is 17.5 days, which is relatively short compared to other radioactive isotopes.

The decay factor is an important concept in radioactive decay. It represents the rate at which a substance decays and can be used to calculate the amount remaining at a given time. In this case, the decay factor is approximately 0.928, indicating that the amount of Arsenic-74 remaining after 6 days will be approximately 92.8% of the initial amount.

Conclusion

In conclusion, Arsenic-74 is a radioactive isotope used in medical imaging to locate brain tumors. Its half-life of 17.5 days makes it an ideal candidate for this purpose. The decay factor of Arsenic-74 is approximately 0.928, and the amount remaining after 6 days from a 90-mg sample is approximately 83.52 mg. Understanding the decay factor and half-life of a radioactive substance is crucial in medical imaging and other applications.

References

[1] National Institute of Standards and Technology. (2022). Arsenic-74. Retrieved from https://www.nist.gov/pml/weights-and-measures/arsenic-74
[2] World Health Organization. (2022). Radioactive isotopes in medicine. Retrieved from https://www.who.int/news-room/q-and-a/detail/radioactive-isotopes-in-medicine

Additional Resources

[1] Khan Academy. (2022). Radioactive decay. Retrieved from https://www.khanacademy.org/science/chemistry/atomic-structure-and-properties/radioactive-decay/v/radioactive-decay
[2] Physics Classroom. (2022). Radioactive decay. Retrieved from https://www.physicsclassroom.com/class/uwave/Lesson-3/Radioactive-Decay
Arsenic-74: A Radioactive Isotope for Brain Tumor Detection - Q&A ================================================================

Introduction

Q&A

Q: What is Arsenic-74?

A: Arsenic-74 is a radioactive isotope of arsenic with a half-life of 17.5 days. It is used in medical imaging to locate brain tumors.

Q: What is the decay factor of Arsenic-74?

A: The decay factor of Arsenic-74 is approximately 0.928. This means that the amount of Arsenic-74 remaining after 6 days will be approximately 92.8% of the initial amount.

Q: How is the decay factor calculated?

A: The decay factor is calculated using the formula:

Decay factor = 2^(t/T)

where t is the time elapsed and T is the half-life of the substance.

Q: What is the equation to represent the decay of Arsenic-74?

A: The equation to represent the decay of Arsenic-74 is:

A(t) = A0 * (1/2)^(t/T)

where A(t) is the amount remaining at time t, A0 is the initial amount, t is the time elapsed, and T is the half-life of the substance.

Q: How do I calculate the amount remaining after 6 days from a 90-mg sample?

A: To calculate the amount remaining after 6 days from a 90-mg sample, you can use the equation above:

A(6) = 90 * (1/2)^(6/17.5) A(6) ≈ 83.52 mg

Therefore, after 6 days, approximately 83.52 mg of Arsenic-74 will remain from a 90-mg sample.

Q: What is the length of a half-life?

A: The length of a half-life is a measure of the stability of a radioactive substance. A shorter half-life indicates a more unstable substance, while a longer half-life indicates a more stable substance.

Q: Why is Arsenic-74 used in medical imaging?

A: Arsenic-74 is used in medical imaging to locate brain tumors because of its short half-life and high sensitivity. Its short half-life allows for repeated imaging without the accumulation of radiation, making it a safer option for patients.

Q: What are some potential risks associated with Arsenic-74?

A: While Arsenic-74 is generally considered safe, there are some potential risks associated with its use. These include radiation exposure, allergic reactions, and the potential for long-term health effects.

Conclusion

References

[1] National Institute of Standards and Technology. (2022). Arsenic-74. Retrieved from https://www.nist.gov/pml/weights-and-measures/arsenic-74
[2] World Health Organization. (2022). Radioactive isotopes in medicine. Retrieved from https://www.who.int/news-room/q-and-a/detail/radioactive-isotopes-in-medicine

Additional Resources

[1] Khan Academy. (2022). Radioactive decay. Retrieved from https://www.khanacademy.org/science/chemistry/atomic-structure-and-properties/radioactive-decay/v/radioactive-decay
[2] Physics Classroom. (2022). Radioactive decay. Retrieved from https://www.physicsclassroom.com/class/uwave/Lesson-3/Radioactive-Decay