Niobium-91 Has A Half-life Of 680 Years. After 2,040 Years, How Much Niobium-91 Will Remain From A 300.0-g Sample?A. 3 G B. 18.75 G C. 37.5 G D. 100.0 G
Introduction
Radioactive decay is a process in which unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This process is a fundamental aspect of nuclear physics and has numerous applications in various fields, including medicine, energy production, and materials science. In this article, we will explore the concept of radioactive decay using the example of niobium-91, a radioactive isotope with a half-life of 680 years.
Radioactive Decay and Half-Life
Radioactive decay is a first-order process, meaning that the rate of decay is directly proportional to the amount of the radioactive substance present. The half-life of a radioactive isotope is the time required for half of the initial amount of the substance to decay. In the case of niobium-91, the half-life is 680 years, which means that every 680 years, the amount of niobium-91 will decrease by half.
Calculating the Remaining Amount of Niobium-91
To calculate the remaining amount of niobium-91 after a certain period, we can use the formula for radioactive decay:
A = A0 * (1/2)^(t/T)
Where:
- A is the remaining amount of the substance
- A0 is the initial amount of the substance
- t is the time elapsed
- T is the half-life of the substance
In this case, we are given the initial amount of niobium-91 as 300.0 g and the time elapsed as 2,040 years. We need to calculate the remaining amount of niobium-91 after 2,040 years.
Step 1: Convert the Time Elapsed to Half-Lives
To use the formula for radioactive decay, we need to convert the time elapsed to half-lives. We can do this by dividing the time elapsed by the half-life:
t/T = 2040 years / 680 years = 3 half-lives
Step 2: Calculate the Remaining Amount of Niobium-91
Now that we have the time elapsed in half-lives, we can plug in the values into the formula for radioactive decay:
A = A0 * (1/2)^(t/T) = 300.0 g * (1/2)^3 = 300.0 g * 1/8 = 37.5 g
Therefore, after 2,040 years, there will be 37.5 g of niobium-91 remaining from the initial 300.0 g sample.
Conclusion
In this article, we explored the concept of radioactive decay using the example of niobium-91. We calculated the remaining amount of niobium-91 after 2,040 years using the formula for radioactive decay. The result shows that there will be 37.5 g of niobium-91 remaining from the initial 300.0 g sample. This calculation demonstrates the importance of understanding radioactive decay in various fields, including medicine, energy production, and materials science.
References
- [1] National Institute of Standards and Technology. (2022). Radioactive Decay.
- [2] University of California, Berkeley. (2022). Radioactive Decay.
- [3] World Nuclear Association. (2022). Radioactive Decay.
Frequently Asked Questions
- Q: What is the half-life of niobium-91? A: The half-life of niobium-91 is 680 years.
- Q: How much niobium-91 will remain after 2,040 years from a 300.0 g sample? A: There will be 37.5 g of niobium-91 remaining from the initial 300.0 g sample.
- Q: What is the formula for radioactive decay?
A: The formula for radioactive decay is A = A0 * (1/2)^(t/T).
Frequently Asked Questions: Radioactive Decay =============================================
Q: What is radioactive decay?
A: Radioactive decay is a process in which unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This process is a fundamental aspect of nuclear physics and has numerous applications in various fields, including medicine, energy production, and materials science.
Q: What is the half-life of a radioactive substance?
A: The half-life of a radioactive substance is the time required for half of the initial amount of the substance to decay. It is a measure of the rate of decay and is typically denoted by the symbol T.
Q: How is the half-life of a radioactive substance determined?
A: The half-life of a radioactive substance is determined by measuring the rate of decay and using the formula for radioactive decay: A = A0 * (1/2)^(t/T), where A is the remaining amount of the substance, A0 is the initial amount of the substance, t is the time elapsed, and T is the half-life of the substance.
Q: What is the formula for radioactive decay?
A: The formula for radioactive decay is A = A0 * (1/2)^(t/T), where A is the remaining amount of the substance, A0 is the initial amount of the substance, t is the time elapsed, and T is the half-life of the substance.
Q: How is the rate of decay affected by the half-life of a radioactive substance?
A: The rate of decay is directly proportional to the half-life of a radioactive substance. A shorter half-life means a faster rate of decay, while a longer half-life means a slower rate of decay.
Q: What are some examples of radioactive decay?
A: Some examples of radioactive decay include:
- Uranium-238 decaying into thorium-234
- Radium-226 decaying into radon-222
- Carbon-14 decaying into nitrogen-14
Q: What are some applications of radioactive decay?
A: Some applications of radioactive decay include:
- Medicine: Radioactive decay is used in medical imaging and cancer treatment
- Energy production: Radioactive decay is used in nuclear power plants to generate electricity
- Materials science: Radioactive decay is used to study the properties of materials and to develop new materials
Q: What are some safety precautions when working with radioactive materials?
A: Some safety precautions when working with radioactive materials include:
- Wearing protective clothing and equipment
- Following proper handling and storage procedures
- Minimizing exposure to radiation
- Monitoring radiation levels and taking corrective action if necessary
Q: What are some common sources of radiation?
A: Some common sources of radiation include:
- Nuclear power plants
- Medical facilities
- Industrial facilities
- Natural sources (e.g. cosmic rays, radon in soil)
Q: How can I protect myself from radiation?
A: You can protect yourself from radiation by:
- Following proper safety procedures when working with radioactive materials
- Wearing protective clothing and equipment
- Minimizing exposure to radiation
- Monitoring radiation levels and taking corrective action if necessary
Q: What are some common myths about radiation?
A: Some common myths about radiation include:
- Radiation is always bad and should be avoided at all costs
- Radiation is only used in nuclear power plants and medical facilities
- Radiation is not a natural occurrence
Q: What are some common misconceptions about radioactive decay?
A: Some common misconceptions about radioactive decay include:
- Radioactive decay is a random process
- Radioactive decay is only affected by the half-life of a substance
- Radioactive decay is not a natural occurrence
Conclusion
Radioactive decay is a fundamental aspect of nuclear physics and has numerous applications in various fields. Understanding the concept of radioactive decay and its applications can help you make informed decisions and stay safe when working with radioactive materials.