The Half-life Of A Particular Radioactive Substance Is 10 Seconds. If You Started With 4120 Grams Of This Substance, How Much Of It Would Remain After 60 Seconds?Use The Formula: Remaining Amount = I ( 1 − R ) T I(1-r)^t I ( 1 − R ) T Round Your Answer To The Nearest
Introduction
Radioactive substances are known to decay over time, releasing energy in the form of radiation. The half-life of a radioactive substance is the time it takes for half of the initial amount to decay. In this article, we will explore the concept of half-life and how it can be used to calculate the remaining amount of a radioactive substance after a certain period of time.
What is Half-Life?
The half-life of a radioactive substance is a fundamental concept in nuclear physics. It is defined as the time it takes for half of the initial amount of the substance to decay. The half-life is a constant value that depends on the specific radioactive substance and is typically denoted by the symbol "t1/2".
Calculating the Remaining Amount
To calculate the remaining amount of a radioactive substance after a certain period of time, we can use the formula:
Remaining Amount = Initial Amount x (1/2)^(t/t1/2)
Where:
- Initial Amount is the initial amount of the substance
- t is the time elapsed
- t1/2 is the half-life of the substance
However, in this case, we will use the formula: Remaining Amount = I(1-r)^t where I is the initial amount, r is the decay rate, and t is the time elapsed.
Calculating the Decay Rate
To calculate the decay rate, we need to know the half-life of the substance. In this case, the half-life is given as 10 seconds. We can use the formula:
r = 1 - (1/2)^(1/t1/2)
Where:
- r is the decay rate
- t1/2 is the half-life of the substance
Plugging in the values, we get:
r = 1 - (1/2)^(1/10) = 0.0952
Calculating the Remaining Amount
Now that we have the decay rate, we can calculate the remaining amount of the substance after 60 seconds. We will use the formula:
Remaining Amount = I(1-r)^t
Where:
- I is the initial amount (4120 grams)
- r is the decay rate (0.0952)
- t is the time elapsed (60 seconds)
Plugging in the values, we get:
Q: What is the half-life of a radioactive substance?
A: The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. It is a fundamental concept in nuclear physics and is typically denoted by the symbol "t1/2".
Q: How is the half-life of a radioactive substance calculated?
A: The half-life of a radioactive substance can be calculated using the formula:
r = 1 - (1/2)^(1/t1/2)
Where:
- r is the decay rate
- t1/2 is the half-life of the substance
Q: What is the decay rate of a radioactive substance?
A: The decay rate of a radioactive substance is the rate at which the substance decays. It is typically denoted by the symbol "r" and is a value between 0 and 1.
Q: How is the remaining amount of a radioactive substance calculated?
A: The remaining amount of a radioactive substance can be calculated using the formula:
Remaining Amount = I(1-r)^t
Where:
- I is the initial amount of the substance
- r is the decay rate
- t is the time elapsed
Q: What is the relationship between the half-life and the decay rate of a radioactive substance?
A: The half-life and the decay rate of a radioactive substance are related by the formula:
r = 1 - (1/2)^(1/t1/2)
This formula shows that the decay rate is inversely proportional to the half-life of the substance.
Q: How does the half-life of a radioactive substance affect its decay rate?
A: The half-life of a radioactive substance affects its decay rate in the following way:
- A shorter half-life means a faster decay rate
- A longer half-life means a slower decay rate
Q: What is the significance of the half-life of a radioactive substance in real-world applications?
A: The half-life of a radioactive substance is significant in real-world applications such as:
- Nuclear power generation
- Medical imaging
- Radiation therapy
- Environmental monitoring
Q: Can the half-life of a radioactive substance be changed?
A: No, the half-life of a radioactive substance cannot be changed. It is a fundamental property of the substance and is determined by its nuclear structure.
Q: How can the remaining amount of a radioactive substance be measured?
A: The remaining amount of a radioactive substance can be measured using various methods such as:
- Gamma-ray spectroscopy
- Beta-ray spectroscopy
- Alpha-ray spectroscopy
- Neutron activation analysis
Q: What are some common applications of the half-life of radioactive substances?
A: Some common applications of the half-life of radioactive substances include:
- Nuclear power generation
- Medical imaging
- Radiation therapy
- Environmental monitoring
- Dating of archaeological samples
Q: Can the half-life of a radioactive substance be used to determine its age?
A: Yes, the half-life of a radioactive substance can be used to determine its age. This is known as radiometric dating and is used to date archaeological samples, rocks, and other materials.
Q: What are some common sources of radioactive substances?
A: Some common sources of radioactive substances include:
- Uranium
- Thorium
- Radium
- Radon
- Carbon-14
Q: How can the half-life of a radioactive substance be used to predict its future behavior?
A: The half-life of a radioactive substance can be used to predict its future behavior by using the formula:
Remaining Amount = I(1-r)^t
This formula shows that the remaining amount of the substance decreases exponentially with time, and can be used to predict the future behavior of the substance.