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

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    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

    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


    • Table 14.4: “T-Chart” (CC-BY 4.0; Chloe Branciforte, own work)
    • Figure 14.25: “Half-life Curve Graph” (CC-BY 4.0; Chloe Branciforte, own work)

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