From the calculation, the age of the sample of carbon - 14 is 9156 years.
The term radioactivity refers to the fact that a substance could disintegrate spontaneously when left alone.
Now, given that;
0.693/t1/2 = 2.303/t log (No/N)
t1/2 = half life
t = age of the sample
No = amount of sample originally present
N = amount of sample present at time t
Hence;
0.693/5730 = 2.303/t log (9216/3072)
1.2 * 10^-4 = 2.303/t * 0.4771
1.2 * 10^-4 = 1.09876/t
t = 1.09876/1.2 * 10^-4
t = 9156 years
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