Half life worksheet with answers – Embark on an educational journey with our half-life worksheet with answers, meticulously crafted to illuminate this intriguing concept. Whether you’re a student seeking to conquer half-life calculations or a professional seeking a refresher, this worksheet will guide you every step of the way.
Delve into the fascinating world of half-life, where radioactive elements decay and medical treatments unfold. Our comprehensive worksheet empowers you to unravel the mysteries of half-life and apply your newfound knowledge in real-world scenarios.
Introduction
Half-life refers to the time it takes for a substance to reduce to half of its original quantity. It’s a fundamental concept in various fields, including chemistry, medicine, and environmental science.
This worksheet aims to provide an understanding of half-life, its formula, and its applications. It’s intended for students and individuals seeking to enhance their knowledge of this important concept.
Formula for Half-Life
The formula for calculating half-life (t 1/2) is:
t1/2= (ln 2) / k
Where:
- ln is the natural logarithm
- k is the rate constant
Half-Life Calculations
The half-life of a substance is the time it takes for half of the substance to decay or transform. It is a measure of the stability of a substance. The formula for calculating half-life is:“`Half-life = ln(2) / Decay constant (λ)“`where:* ln(2) is the natural logarithm of 2, which is approximately 0.693
Decay constant (λ) is a constant that describes the rate of decay of the substance
Example Problems, Half life worksheet with answers
A radioactive isotope has a decay constant of 0.005 per year. What is its half-life?“`Half-life = ln(2) / 0.005 per year= 138.6 years“`A drug has a half-life of 6 hours. If you take 100 mg of the drug, how much will remain in your system after 12 hours?“`After 12 hours, the amount of drug remaining will be:
- mg
- (1/2)^(12 hours / 6 hours)
= 100 mg
(1/2)^2
= 25 mg“`
Applications of Half-Life
Half-life finds applications in various fields, primarily in radioactive decay and medical treatments. It helps us understand the decay rates of radioactive substances and determine the effectiveness of medical treatments over time.
Radioactive Decay
Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. The half-life of a radioactive substance represents the time it takes for half of its atoms to decay. This information is crucial in:
- Nuclear Power:Determining the rate at which nuclear fuel decays helps optimize reactor operations and ensure safety.
- Waste Management:Understanding the half-lives of radioactive waste products aids in designing safe storage and disposal facilities.
- Radioactive Dating:Measuring the half-lives of radioactive isotopes in geological samples helps determine the age of rocks, fossils, and artifacts.
Medical Treatments
Half-life plays a vital role in medical treatments involving radioactive substances. It determines:
- Radiotherapy:The half-life of radioactive isotopes used in radiation therapy influences the duration and effectiveness of cancer treatment.
- Drug Delivery:Controlled-release drug delivery systems utilize substances with specific half-lives to ensure a sustained release of medication over time.
li> Diagnostic Imaging:Radioactive tracers with known half-lives are used in medical imaging techniques like PET and SPECT scans to track metabolic processes and diagnose diseases.
Half-Life Practice Problems
Test your understanding of half-life calculations with these practice problems. These problems cover various scenarios to assess your grasp of the concept.
Each problem provides an opportunity to apply the half-life formula and demonstrate your ability to determine the remaining amount of a substance after a given time or calculate the time required for a substance to decay to a specific amount.
Practice Problems
- A radioactive isotope has a half-life of 10 days. If you start with 100 grams of the isotope, how much will remain after 20 days?
- A medicine has a half-life of 6 hours. If you take a 100 mg dose, how much will be left in your system after 18 hours?
- A carbon-14 sample has an activity of 500 counts per minute (cpm). If the half-life of carbon-14 is 5,730 years, how old is the sample?
- A population of bacteria doubles every 24 hours. If there are initially 1000 bacteria, how many will there be after 5 days?
- A chemical reaction has a half-life of 30 minutes. If the initial concentration of the reactant is 1 M, what will be the concentration after 90 minutes?
Answer Key: Half Life Worksheet With Answers
The answer key provides detailed solutions to the half-life practice problems, explaining the reasoning behind each step.
The following sections will present the answers and explanations for each problem.
Problem 1
Calculate the half-life of a radioactive isotope with an initial activity of 100 Bq and an activity of 50 Bq after 10 days.
- Solution:
Using the formula for half-life: t 1/2= (ln2) / k
Where k is the decay constant, which can be calculated using the formula: k = (ln(A 0) – ln(A t)) / t
Plugging in the given values:
k = (ln(100) – ln(50)) / 10 = 0.0693 day -1
Therefore, the half-life is:
t 1/2= (ln2) / k = (ln2) / 0.0693 = 10 days
Problem 2
A sample of carbon-14 has an activity of 8000 Bq. If the half-life of carbon-14 is 5730 years, determine how many years will pass until the activity is reduced to 1000 Bq.
- Solution:
Using the formula for radioactive decay: A t= A 0– (1/2) (t/t1/2)
Where:
A tis the activity at time t
A 0is the initial activity
t is the time elapsed
t 1/2is the half-life
Plugging in the given values:
1000 = 8000 – (1/2) (t/5730)
Solving for t:
t = 5730 – log 2(8) = 12,598 years
Problem 3
A patient is injected with 10 mCi of a radioactive tracer with a half-life of 6 hours. How much of the tracer will remain in the patient’s body after 18 hours?
- Solution:
Using the formula for radioactive decay:
A t= A 0– (1/2) (t/t1/2)
Where:
A tis the activity at time t
A 0is the initial activity
t is the time elapsed
t 1/2is the half-life
Plugging in the given values:
A t= 10 – (1/2) (18/6)= 10 – (1/2) 3= 1.25 mCi
Answers to Common Questions
What is half-life?
Half-life refers to the time it takes for a substance to reduce to half of its initial quantity.
How do I calculate half-life?
Use the formula: Half-life = (0.693 – Initial amount) / Decay constant
What are some real-world applications of half-life?
Half-life finds applications in radioactive decay, medical treatments, and environmental science.
