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What is the Average Life of a Radioactive Sample?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
The 'average life' (or mean life) of a radioactive sample is the average time for which an atom of a radioactive substance exists before it decays. It's like finding the average age of all people in a group before they pass away. It is the reciprocal of the decay constant.
Simple Example
Quick Example
Imagine you have 100 laddoos, and each laddoo has a 'shelf life' before it spoils. Some spoil quickly, some last longer. The average life is like finding the average time all these 100 laddoos lasted before spoiling, giving you an idea of the typical time a laddoo from that batch would stay fresh.
Worked Example
Step-by-Step
Let's calculate the average life of a radioactive isotope if its decay constant is 0.05 per second.
Step 1: Understand the formula. Average life (τ) is given by 1 / (decay constant).
---Step 2: Identify the given value. The decay constant (λ) = 0.05 per second.
---Step 3: Apply the formula. τ = 1 / λ
---Step 4: Substitute the value. τ = 1 / 0.05
---Step 5: Calculate the result. τ = 20 seconds.
---Answer: The average life of the radioactive sample is 20 seconds.
Why It Matters
Understanding average life is crucial in fields like medicine for deciding dosages in radiation therapy, and in space technology for powering probes using radioisotopes. Engineers use this to design safe nuclear reactors and even in climate science to study ancient samples. It can lead to careers in medical physics or nuclear engineering.
Common Mistakes
MISTAKE: Confusing average life with half-life. | CORRECTION: Half-life is the time for HALF the sample to decay, while average life is the average time a single atom exists before decaying. They are related but different values.
MISTAKE: Forgetting the units or using incorrect units for average life. | CORRECTION: Since average life is a measure of time, its unit should be a time unit like seconds, minutes, hours, or years, consistent with the decay constant's unit (e.g., per second).
MISTAKE: Calculating average life by simply dividing the total time by the number of atoms. | CORRECTION: Average life is mathematically defined as the reciprocal of the decay constant (1/λ), not a simple arithmetic average of individual decay times, which would be practically impossible to measure.
Practice Questions
Try It Yourself
QUESTION: If the decay constant of a radioactive substance is 0.1 per year, what is its average life? | ANSWER: 10 years
QUESTION: A radioactive isotope has a decay constant of 0.002 per day. Calculate its average life in days. | ANSWER: 500 days
QUESTION: The half-life of a radioactive material is 6.93 years. Find its decay constant first, then calculate its average life. (Hint: half-life = 0.693 / decay constant) | ANSWER: Decay constant (λ) = 0.1 per year; Average life (τ) = 10 years
MCQ
Quick Quiz
What is the relationship between the average life (τ) and the decay constant (λ) of a radioactive sample?
τ = λ
τ = 1 / λ
τ = λ^2
τ = 0.693 / λ
The Correct Answer Is:
B
The average life is defined as the reciprocal of the decay constant. Option D relates to half-life, not average life.
Real World Connection
In the Real World
In India, radioactive isotopes like Cobalt-60 are used in hospitals for cancer treatment. Scientists and doctors need to know the average life of these isotopes to calculate how long they will remain effective and how to safely handle and dispose of them after use. This ensures patient safety and proper waste management.
Key Vocabulary
Key Terms
RADIOACTIVE: Emitting radiation as a result of atomic decay | DECAY CONSTANT: A measure of the probability of a nucleus decaying per unit time | HALF-LIFE: The time taken for half of the radioactive nuclei in a sample to decay | ISOTOPE: Atoms of the same element with different numbers of neutrons | RECIPROCAL: The inverse of a number (1 divided by the number)
What's Next
What to Learn Next
Next, you should explore 'Radioactive Half-Life' and 'Decay Law'. Understanding half-life will help you see how it relates to average life and how we predict the amount of radioactive material remaining over time, which is super important for many real-world applications!
