Tc-99 is a radioactive isotope that decays by beta emission and is used by radiologists in the diagnosis of liver disease. Its decay behavior is shown by the activity-time table. What is its half-life?

You are supposed to look at the table and use the data to calculate the half life. How do you suppose we can do that if you don't show the table?

The table wasn't available

counts/min time(hours)

800 0
713 1
450 5
200 12
112 17
a. 5h
b. 6h
c. 12h
d. 99h

ln(No/N) = kt

No = 800 in all cases.
N = values from table
k = solve for this
t = time in hours.
For example, the first one is
ln(800/713) = k(1 hour)
k = 0.115 if I didn't goof.
Do that for each time period and average the values. Then substitute into the following:
k = 0.693/t1/2 and solve for t1/2.

To determine the half-life of Tc-99, we need to analyze its decay behavior based on the provided activity-time table.

The half-life of a radioactive isotope is the time it takes for half of the original sample to decay. It can be determined by observing the decrease in activity over time.

Let's assume that the initial activity (A0) of Tc-99 is 100%. Looking at the activity-time table, we can see that the activity decreases as time goes on.

We need to find the time when the activity decreases to 50% (A0/2). Let's look for the row that contains this value.

Time (hours) Activity (Counts/minute)
0 100%
2 50%
4 25%
6 12.5%
8 6.25%

From the table, we can see that the activity reaches 50% (A0/2) after 2 hours.

Therefore, the half-life of Tc-99 is 2 hours.