Activity of a radioactive substance decreases from 8000BQ ato 1000Bq in 9 days.What is half life and average life of radoactive substance

To determine the half-life and average life of a radioactive substance that decreases from 8000 Bq to 1000 Bq in 9 days, we can use some fundamental concepts of radioactivity. Let's break this down step by step.

Understanding Half-Life

The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. In this case, we need to find out how many half-lives it takes for the activity to decrease from 8000 Bq to 1000 Bq.

Calculating the Number of Half-Lives

We start with an initial activity of 8000 Bq. The activity decreases to 1000 Bq. To find out how many half-lives have passed, we can set up the following equation:

• After 1 half-life: 8000 Bq → 4000 Bq
• After 2 half-lives: 4000 Bq → 2000 Bq
• After 3 half-lives: 2000 Bq → 1000 Bq

From this, we can see that it takes 3 half-lives for the activity to drop from 8000 Bq to 1000 Bq.

Finding the Half-Life

Since we know that these 3 half-lives occur over a total time of 9 days, we can calculate the duration of one half-life:

Half-life (T_1/2) = Total time / Number of half-lives

Substituting the values:

T_1/2 = 9 days / 3 = 3 days

Average Life of the Radioactive Substance

The average life (or mean life) of a radioactive substance is related to its half-life. The average life (τ) can be calculated using the formula:

τ = T_1/2 / ln(2)

Where ln(2) is approximately 0.693. Now, substituting the half-life we found:

τ = 3 days / 0.693 ≈ 4.33 days

Summary of Results

In summary, for the radioactive substance that decreases from 8000 Bq to 1000 Bq in 9 days:

• Half-life: 3 days
• Average life: Approximately 4.33 days

This understanding of half-life and average life is crucial in fields like nuclear medicine, radiometric dating, and understanding the behavior of radioactive materials in various applications.