the half-life of carbon-14 is 5700 years. Find the age to the nearest year of a sample in which 16% of the radioactive nuclie originally present have decayed.

Question

I would like the answer and steps to how to get that answer!

Answer 1

N(t) = N₀·(0.5)^t/h

1. N(t) = Number of Nuclei left at time t = 0.16·N₀
2. t = time
3. N0 = starting amount of Nuclei
4. h = half-life= 5700 years

N(t) = N₀·(0.5)^t/h

0.16N₀ = N₀·(0.5)^t/5700

0.16 = (0.5)^t/5700

log(0.16) = log(0.5^t/5700)

log(0.16) = t/5700 · log(0.5) [log property: log(a^b) = b log(a)]

5700·log(0.16)/log(0.5) = t

Use your calculator to get the answer. You can use any base log.