The half-life of carbon-14 is about 5700 years. If you left those 100 carbon-14 atoms to sit around for 5700 years, how many would you expect to decay during that time?

50 atoms of carbon-14

Explanation:

From the question given above, the following data were obtained:

Original amount (N₀) = 100 atoms

Half-life (t½) = 5700 years

Time (t) = 5700 years

Amount that decay =?

Next, we shall determine the number of half-lives that has elapse. This can be obtained illustrated below:

Half-life (t½) = 5700 years

Time (t) = 5700 years

Number of half-lives (n) =?

n = t / t½

n = 5700 / 5700

n = 1

Next, we shall determine the amount remaining. This can be obtained as follow:

Original amount (N₀) = 100 atoms

Number of half-lives (n) = 1

Amount remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2¹ × 100

N = 1/2 × 100

N = 50 atoms

Finally, we shall determine the amount that decayed as follow:

Original amount (N₀) = 100 atoms

Amount remaining (N) = 50 atoms

Amount that decay =?

Amount that decay = N₀ – N

Amount that decay = 100 – 50

Amount that decay = 50 atoms

Therefore, 50 atoms of carbon-14 have decayed during the time.