Answer:
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.
