Looking at the graph, I can see it's a plot of "Counts per minute" on the y-axis against "Time in days" on the x-axis. The curve shows exponential decay, which is typical for radioactive decay. The graph explicitly marks three points corresponding to 1, 2, and 3 half-lives.
To solve the problem, I need to determine the half-life of the substance from this graph. The half-life is the time it takes for the activity (counts per minute) to reduce to half its initial value.
I can read the values directly from the graph:
- At time t=0, the initial count rate is 300 counts per minute.
- After one half-life, the count rate should be half of 300, which is 150 counts per minute. The red dashed line indicates this point occurs at approximately 9 days.
- After two half-lives, the count rate should be half of 150, which is 75 counts per minute. The blue dashed line indicates this point occurs at approximately 18 days.
- After three half-lives, the count rate should be half of 75, which is 37.5 counts per minute. The green dashed line indicates this point occurs at approximately 27 days.
The half-life can be calculated by finding the time interval between these points:
- From 0 to 1 half-life: 9 days - 0 days = 9 days
- From 1 to 2 half-lives: 18 days - 9 days = 9 days
- From 2 to 3 half-lives: 27 days - 18 days = 9 days
All intervals are consistent, confirming that the half-life is 9 days.
Therefore, the solution to the problem is that the half-life of the radioactive substance shown in the graph is 9 days.
Parent Tip: Review the logic above to help your child master the concept of half life graph worksheet.
