Carbon-14 has a half-life of 5730 years. in a plant fossil, you find that the 14c has decayed to 1/4.00 of the original amount. how long ago was this plant alive?

We use the radioactive decay formula to solve this problem. It is expressed as:

An = Aoe^-kt

where An is the amount left in time t, Ao is the initial amount, k is the constant.

We first find the value of k from the half-life data. We do as follows:

An = Aoe^-kt
0.5 = e^-k(5730)
k = 1.21x10^-4

An = Aoe^-kt
1/4 = e^-1.21x10^-4t
t = 11456.98 years

Most smaller stars don't have a radiative zone.

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