Half-Life Calculations Worksheet With Answers: Quick Guide
Table of Contents :
Half-life calculations are essential in various fields, particularly in chemistry, physics, and environmental science. Understanding half-life is crucial for predicting the decay of substances, be it radioactive elements or even certain drugs in the human body. In this guide, we will explore half-life calculations, provide a worksheet, and present the answers for a better comprehension of the topic. Let's delve into the world of half-lives! 🧪
What is Half-Life?
Half-life is defined as the time taken for the quantity of a substance to reduce to half its initial amount. This concept is vital for understanding radioactive decay and other processes that involve exponential decay.
Key Points to Remember
- Exponential Decay: The quantity decreases at a rate proportional to its current value.
- Constant Rate: The half-life remains constant regardless of the initial amount of the substance.
- Applications: Radioactive dating, pharmacokinetics, and environmental studies.
Half-Life Formula
The half-life can be calculated using the formula:
[ N_t = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} ]
Where:
- (N_t) = remaining quantity after time (t)
- (N_0) = initial quantity
- (t) = time elapsed
- (t_{1/2}) = half-life of the substance
Half-Life Calculation Worksheet
Here’s a quick worksheet to practice half-life calculations. Fill in the blanks using the above formula.
Worksheet Questions
| Question No. | Initial Quantity (N0) | Half-Life (t1/2) | Time Elapsed (t) | Remaining Quantity (Nt) |
|---|---|---|---|---|
| 1 | 80 g | 5 years | 15 years | ? |
| 2 | 200 g | 10 days | 30 days | ? |
| 3 | 50 g | 1 year | 4 years | ? |
| 4 | 1000 g | 2 hours | 10 hours | ? |
| 5 | 160 g | 8 hours | 32 hours | ? |
Important Notes
"When performing half-life calculations, ensure that the time elapsed is expressed in the same units as the half-life."
Answers to the Worksheet
Now let's calculate the remaining quantities for each question using the half-life formula.
Solution Table
| Question No. | Initial Quantity (N0) | Half-Life (t1/2) | Time Elapsed (t) | Remaining Quantity (Nt) |
|---|---|---|---|---|
| 1 | 80 g | 5 years | 15 years | 10 g |
| 2 | 200 g | 10 days | 30 days | 50 g |
| 3 | 50 g | 1 year | 4 years | 3.125 g |
| 4 | 1000 g | 2 hours | 10 hours | 62.5 g |
| 5 | 160 g | 8 hours | 32 hours | 10 g |
Explanation of Answers
-
Question 1: After 15 years (which is 3 half-lives), the calculation is: [ N_t = 80 \left( \frac{1}{2} \right)^{\frac{15}{5}} = 80 \left( \frac{1}{2} \right)^{3} = 80 \times \frac{1}{8} = 10 , g ]
-
Question 2: For 30 days (which is 3 half-lives), the calculation is: [ N_t = 200 \left( \frac{1}{2} \right)^{\frac{30}{10}} = 200 \left( \frac{1}{2} \right)^{3} = 200 \times \frac{1}{8} = 25 , g ]
-
Question 3: For 4 years (which is 4 half-lives), the calculation is: [ N_t = 50 \left( \frac{1}{2} \right)^{\frac{4}{1}} = 50 \left( \frac{1}{2} \right)^{4} = 50 \times \frac{1}{16} = 3.125 , g ]
-
Question 4: For 10 hours (which is 5 half-lives), the calculation is: [ N_t = 1000 \left( \frac{1}{2} \right)^{\frac{10}{2}} = 1000 \left( \frac{1}{2} \right)^{5} = 1000 \times \frac{1}{32} = 31.25 , g ]
-
Question 5: For 32 hours (which is 4 half-lives), the calculation is: [ N_t = 160 \left( \frac{1}{2} \right)^{\frac{32}{8}} = 160 \left( \frac{1}{2} \right)^{4} = 160 \times \frac{1}{16} = 10 , g ]
Conclusion
Mastering half-life calculations is crucial for various scientific applications. By practicing through worksheets and analyzing answers, you can reinforce your understanding of this concept. With the skills acquired from this guide, you're now equipped to tackle half-life problems with confidence. 🧠