A Certain Compound Has A Half-life Of 3 Days. If The Initial Amount Of The Compound Is 15 Grams, How Many Grams Will Remain After 17 Days?Given:$\[ Y = 360(1-0.15)^5 \\]$\[ U = 15(1-0.03)^{17} \\]Calculate The Remaining Amount After

Introduction

In chemistry, the concept of half-life is crucial in understanding the decay of radioactive substances. The half-life of a substance is the time it takes for half of the initial amount to decay. In this article, we will explore how to calculate the remaining amount of a compound after a certain period, given its half-life and initial amount.

Understanding Half-Life

The half-life of a substance is a fundamental concept in nuclear physics and chemistry. It is the time required for half of the initial amount of a radioactive substance to decay. The half-life is a constant value that depends on the properties of the substance and is independent of the initial amount.

Calculating the Remaining Amount

To calculate the remaining amount of a compound after a certain period, we can use the formula:

${ y = A(1 - r)^t }$

where:

• ${ y }$ is the remaining amount
• ${ A }$ is the initial amount
• ${ r }$ is the decay rate (which is 0.5 for a half-life of 3 days)
• ${ t }$ is the time in days

However, in this problem, we are given a different formula:

${ u = 15(1-0.03)^{17} }$

This formula is used to calculate the remaining amount after 17 days, given the initial amount of 15 grams and a decay rate of 0.03.

Calculating the Decay Rate

To calculate the decay rate, we need to know the half-life of the compound. The half-life is given as 3 days. We can use the formula:

${ r = \frac{1}{2}^{\frac{1}{t}} }$

where:

• ${ r }$ is the decay rate
• ${ t }$ is the half-life in days

Plugging in the values, we get:

${ r = \frac{1}{2}^{\frac{1}{3}} }$ ${ r = 0.03 }$

Calculating the Remaining Amount

Now that we have the decay rate, we can plug it into the formula:

${ u = 15(1-0.03)^{17} }$

To calculate the remaining amount, we can use a calculator or a programming language like Python:

import math

# Define the initial amount and decay rate
A = 15
r = 0.03
t = 17

# Calculate the remaining amount
u = A * (1 - r) ** t

print(u)

Running this code, we get:

${ u = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Introduction

In our previous article, we explored how to calculate the remaining amount of a compound after a certain period, given its half-life and initial amount. In this article, we will answer some frequently asked questions related to the concept of half-life and its application in chemistry.

Q: What is half-life?

A: Half-life is the time it takes for half of the initial amount of a radioactive substance to decay. It is a fundamental concept in nuclear physics and chemistry.

Q: How is half-life calculated?

A: Half-life is calculated using the formula:

[ r = \frac{1}{2}^{\frac{1}{t}} }$

where:

• ${ r }$ is the decay rate
• ${ t }$ is the half-life in days

Q: What is the difference between half-life and decay rate?

A: Half-life is the time it takes for half of the initial amount to decay, while decay rate is the rate at which the substance decays. The decay rate is a constant value that depends on the properties of the substance.

Q: How is the remaining amount calculated?

A: The remaining amount is calculated using the formula:

${ y = A(1 - r)^t }$

where:

• ${ y }$ is the remaining amount
• ${ A }$ is the initial amount
• ${ r }$ is the decay rate
• ${ t }$ is the time in days

Q: What is the significance of half-life in chemistry?

A: Half-life is significant in chemistry because it helps us understand the decay of radioactive substances. It is used to calculate the remaining amount of a substance after a certain period and to predict the time it takes for a substance to decay completely.

Q: Can half-life be used to predict the future behavior of a substance?

A: Yes, half-life can be used to predict the future behavior of a substance. By knowing the half-life of a substance, we can calculate the remaining amount after a certain period and predict the time it takes for the substance to decay completely.

Q: What are some real-world applications of half-life?

A: Half-life has many real-world applications, including:

• Nuclear medicine: Half-life is used to calculate the remaining amount of radioactive substances used in medical treatments.
• Environmental science: Half-life is used to predict the time it takes for radioactive substances to decay in the environment.
• Nuclear power: Half-life is used to calculate the remaining amount of radioactive substances in nuclear reactors.

Q: Can half-life be used to calculate the age of a substance?

A: Yes, half-life can be used to calculate the age of a substance. By knowing the half-life of a substance and the remaining amount, we can calculate the time it has been decaying and determine its age.

Conclusion

In conclusion, half-life is a fundamental concept in chemistry that helps us understand the decay of radioactive substances. By knowing the half-life of a substance, we can calculate the remaining amount after a certain period and predict the time it takes for the substance to decay completely. Half-life has many real-world applications, including nuclear medicine, environmental science, and nuclear power.