Half-Life Calculation
The concept of half-life refers to the time it takes for half of the initial amount of a substance (such as a radioactive isotope) to decay. Let's break down the steps for calculating the time based on the given data.
Given Information:
- N1 = 0.6 N0: The quantity of the substance at some point after decay (0.6 times the original amount).
- N2 = 0.15 N0: The quantity of the substance after a further period of time (0.15 times the original amount).
Step 1: Ratio of N2 and N1
We can calculate the ratio between and as follows:
This shows that the ratio is equal to 1/4, meaning that two half-lives have passed. Here’s why:
- In each half-life, the amount of the substance reduces by half. The formula above shows that is 1/4 of the original quantity, which is equivalent to two half-lives.
Step 2: Calculating Time Taken
Now that we know two half-lives have passed, we can calculate the total time taken:
So, the time taken for this process to occur is 60 minutes.
Summary:
Given the decrease from to , we find that two half-lives have passed. Since each half-life is 30 minutes, the total time taken is 60 minutes.