Question

Recall that ¹⁴C has a half life of 5,730 years. To calibrate the x-axis for ¹⁴C decay, write the time before present in years below each half-life.

Short answer

¹⁴C has a half-life of 5,730 years.

Time in years at one half-life would be 5,730.

Step-by-step solution

Step 1:Time in years at one half-life

¹⁴C has a half-life of 5,730 years.

Time in years at one half-life would be 5,730.

Time in years at two half-lives

Years in number of half-lives = Half-life X Number of half-lives

Years at two half-lives$$\begin{gathered} =\text{5,730}\times \text{2} \\ \text{= 11,460} \end{gathered}$$

Time in years at three half-lives

Years at three half-lives $$\begin{gathered} =\text{5,730}\times \text{3} \\ \text{= 17,190} \end{gathered}$$

Time in years at four half-lives

Years at four half-lives$$\begin{gathered} =5,730\times 4 \\ =22,920 \end{gathered}$$

Time in years at five half-lives

Years at five half-lives$$\begin{gathered} =5,730\times 5 \\ =28,650 \end{gathered}$$

Time in years at six half-lives

Years at six half-lives$$\begin{gathered} =5,730\times 6 \\ =34,380 \end{gathered}$$

Time in years at seven half-lives

Years at seven half-loves$$\begin{gathered} =5,730\times 7 \\ =40,110 \end{gathered}$$

Time in years at eight half-lives

Years at eight half-lives$$\begin{gathered} =5,730\times 8 \\ =45,840 \end{gathered}$$

Time in years at nine half-lives

Years at nine half-lives$$\begin{gathered} =5,730\times 9 \\ =51,570 \end{gathered}$$

Time in years at ten half-lives

Years at ten half-lives$$\begin{gathered} =5,730\times 10 \\ =57,300 \end{gathered}$$