after how many years will 1/128g of the original carbon-14 remain
To determine the number of years it will take for 1/128g of the original carbon-14 to remain, we can use the concept of exponential decay.
The half-life of carbon-14 is about 5730 years, which means that after 5730 years, half of the original amount of carbon-14 will have decayed.
To find out how many times the half-life occurs within a given time frame, we can use the formula:
N = (1/2)^(t / h)
Where:
N: The fraction of carbon-14 remaining (in this case, 1/128).
t: The time elapsed.
h: The half-life of carbon-14 (5730 years).
Rearranging the formula to solve for t:
t = -h * log2(N)
Plugging in the values and solving the equation:
t = -5730 * log2(1/128)
Using a calculator:
t ≈ -5730 * log2(1/128)
t ≈ -5730 * log2(1/2^7)
t ≈ -5730 * log2(2^-7)
t ≈ -5730 * (-7)
t ≈ 5730 * 7
t ≈ 40110
Therefore, it will take approximately 40,110 years for 1/128g of the original carbon-14 to remain.