Answer :

To solve the problem of determining the half-life of Au-198, we need to understand how radioactive decay works. The half-life is the time it takes for half of a sample to decay.

Here's how you can find the half-life of Au-198 given the conditions:

1. Identify Initial and Final Amounts:
- The initial amount of Au-198 is 100 grams.
- The final amount of Au-198 is 6.25 grams.

2. Determine the Number of Half-Lives Passed:
- Each half-life reduces the remaining amount to half of its previous value.
- Start with 100 grams; one half-life would reduce it to 50 grams, two half-lives to 25 grams, three half-lives to 12.5 grams, and four half-lives to 6.25 grams.

3. Observe the Time Taken:
- We know it takes 10.8 days for the amount of Au-198 to decrease from 100 grams to 6.25 grams.
- Since four half-lives have passed in these 10.8 days, we use this to find a single half-life.

4. Calculate the Half-Life:
- Divide the total time by the number of half-lives: 10.8 days ÷ 4 = 2.7 days.

This tells us that the half-life of Au-198 is 2.7 days.

Thanks for taking the time to read If 100 grams of Au 198 decays to 6 25 grams in 10 8 days what is the half life of Au 198. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada