Half Life Worksheet Answer Key: Quick Study Guide
Table of Contents :
The study of the half-life of substances is a crucial aspect of chemistry, particularly in nuclear chemistry and radioactivity. Understanding half-life helps students and professionals alike grasp the principles of radioactive decay, which has practical implications in various fields, from medicine to environmental science. In this quick study guide, we’ll explore the concept of half-life, how to calculate it, and provide a worksheet answer key to facilitate your learning.
What is Half-Life? 🕒
Definition: The half-life of a radioactive substance is the time required for half of the substance to decay. This concept is essential for understanding how long radioactive materials remain hazardous and how they behave over time.
Formula for Half-Life
The half-life can be calculated using the following formula:
[ t_{1/2} = \frac{\ln(2)}{\lambda} ]
Where:
- ( t_{1/2} ) = half-life
- ( \lambda ) = decay constant
- ( \ln ) = natural logarithm
Understanding Decay Constant
The decay constant (( \lambda )) is a probability value that represents the likelihood of a particle decaying per unit time. A larger decay constant indicates a faster decay and thus a shorter half-life.
Example Calculations 🧮
To solidify the concept of half-life, let’s consider a few examples.
Example 1: Carbon-14
Carbon-14 (( ^{14}C )) is a common isotope used in dating archaeological finds. Its half-life is approximately 5,730 years.
Calculation: If you start with a sample of 1,000 grams of Carbon-14, the amount remaining after 5,730 years would be:
[ \text{Remaining amount} = \frac{1000}{2} = 500 \text{ grams} ]
After another 5,730 years (11,460 years total), you would have:
[ \text{Remaining amount} = \frac{500}{2} = 250 \text{ grams} ]
Example 2: Uranium-238
Uranium-238 (( ^{238}U )) has a half-life of about 4.5 billion years.
Calculation: If we begin with 1,000 grams of Uranium-238, after 4.5 billion years:
[ \text{Remaining amount} = \frac{1000}{2} = 500 \text{ grams} ]
After another 4.5 billion years (9 billion years total):
[ \text{Remaining amount} = \frac{500}{2} = 250 \text{ grams} ]
Half-Life Table
To assist with calculations, it’s useful to have a reference table. Below is a simplified table of half-lives for various isotopes.
<table> <tr> <th>Isotope</th> <th>Half-Life</th> </tr> <tr> <td>Carbon-14</td> <td>5,730 years</td> </tr> <tr> <td>Uranium-238</td> <td>4.5 billion years</td> </tr> <tr> <td>Radon-222</td> <td>3.8 days</td> </tr> <tr> <td>Iodine-131</td> <td>8.02 days</td> </tr> </table>
Practice Problems and Answer Key 📚
To reinforce your understanding, here are some practice problems along with an answer key.
Practice Problems:
- If you have a 200-gram sample of Polonium-210, which has a half-life of 138 days, how much will remain after 414 days?
- A sample of Strontium-90 weighs 1,000 grams. Its half-life is 29 years. How much will remain after 87 years?
- A certain isotope has a half-life of 10 years. If you start with 160 grams, how much will remain after 30 years?
Answer Key:
-
Polonium-210:
- After 414 days: [ \text{Number of half-lives} = \frac{414 \text{ days}}{138 \text{ days}} \approx 3 ] [ \text{Remaining amount} = \frac{200}{2^3} = 25 \text{ grams} ]
-
Strontium-90:
- After 87 years: [ \text{Number of half-lives} = \frac{87 \text{ years}}{29 \text{ years}} \approx 3 ] [ \text{Remaining amount} = \frac{1000}{2^3} = 125 \text{ grams} ]
-
Unknown Isotope:
- After 30 years: [ \text{Number of half-lives} = \frac{30 \text{ years}}{10 \text{ years}} = 3 ] [ \text{Remaining amount} = \frac{160}{2^3} = 20 \text{ grams} ]
Important Notes 📝
- Context of Half-Life: The concept of half-life not only applies to radioactive decay but also to pharmacokinetics, where it measures the time taken for the concentration of a substance in the body to reduce to half.
- Environmental Impact: Understanding half-lives is critical in dealing with radioactive waste and contamination, as it helps predict the duration hazardous materials might pose a risk to health and safety.
By utilizing this quick study guide, complete with practice problems and an answer key, you should now have a firmer grasp of half-life calculations and their practical applications. This knowledge can be pivotal in various scientific fields and enhance your understanding of the natural world.