If the half-life is 2,000 years, after 11,400 years, the remaining mass would be approximately 0.703 grams.
To calculate the remaining mass of a radioactive substance after a certain period of time, we use the formula for exponential decay:
N = N0 * (1/2)^(t/T)
where:
N is the remaining quantity,
N0 is the initial quantity,
t is the elapsed time,
T is the half-life of the substance.
Given that N0 is 16 grams, we need to know the half-life (T) of the substance. Once we have that information, we can substitute the values into the formula.
For example, if the half-life (T) is 2,000 years, and the elapsed time (t) is 11,400 years, the calculation would be:
N = 16 * (1/2)^(11,400/2,000)
N ≈ 16 * (1/2)^5.7
N ≈ 16 * 0.043945
N ≈ 0.703