# 14.4: Activity 14C - T-charts, Decay Curves, and Half-lives

• • Professors (Geology) at Ventura College & East Los Angeles College
• Sourced from ASCCC Open Educational Resources Initiative

Helpful tips to calculate a half-life:

• Draw or insert a T-chart.
• In the T-chart, label the left side with time units (number of half-lives, years, ka, Ma, Ga, etc.)
• Label right side with mass units (percentage, atoms, gram, kilograms, etc.)
• Begin by ALWAYS writing zero in the first spot of the time column.
• In the mass column, begin with the given mass if provided. Recall that this is 100% of the original parent isotope.
• If the mass is the starting mass, keep dividing the number in the mass column by 2 for each half-life in the left column.
• If you are given a final mass, record this at the very bottom of the mass column.
• If the mass given is the final mass, multiply that mass by 2 until the initial time (Time 0) is reached.
• The final mass amount at the bottom of the mass column equals how much mass is left after radioactive decay has occurred.
• In the time column, add one half-life at a time until you reach the total time given in problem. The number of half-lives elapsed is equal to the number of times you added a half-life in the time column.

1. Calculate the amount of parent isotope remaining for all the given half-lives in this T-chart.

Table 14.4: T-chart to use in question 1-3 in Activity 13C: T-Charts, Decay Curves and Half-lives.

Number of Half-lives

Amount of Parent Isotope Remaining (%)

0

100

1

2

3

4

5

6

7

8

2. Plot your findings from the T-chart on the graph below.

3. Draw the decay curve by connecting your plotted data points. Figure 14.25: Graph to use in question 2-7 in Activity 14C.

Using the above graph (Figure 14.25), answer the following questions.

4. How much of the parent isotope would be remaining after 7 half-lives have passed?

a. 6.25%

b. 1.56%

c. 0.78%

d. 0.39%

5. If a radiometric element has a half-life of 425 years, how old would a rock be that only had 3.125% of the parent isotope remaining?

a. 2125 years

b. 1700 years

c. 2550 years

d. 3400 years

6. Approximately how much of the parent isotope would be remaining after 3.5 half-lives?

a. 16%

b. 12%

c. 4%

d. 8%

7. Based on your graph above, approximately how many half-lives have passed when only 35% of the parent isotope is remaining?

a. 0.75

b. 1.5

c. 2.1

d. 2.5