Question

An animal dies in the forest. How long will it be until only `7/8` of the original amount of Carbon 14 remains?

Recall that the half life of Carbon 14 is 5568 years. Round to the nearest year.

NOTE: The half-life is incorrect. It is 5730 years.
- Truong-Son

Answer 1

`1073` years

Explanation:

All thanks to Truong-Son Nguyen, aka his method!

We use one of the radioactive decay equation, which states that

`[A]=[A]_0e^(-kt)`

• `[A]` is the amount of substance right now

• `[A]_0` is the original amount

• `-k` is the decay constant, and it is negative because the system experiences decay

• `t` is the time in years

We also have half-life, `t_(1/2)`, related by the equation,

`t_(1/2)=(ln 2)/k`

From the original equation, we have `[A]=7/8[A_0]`, and so:

`[A]/[A_0]=7/8=e^(-kt)`

`:.kt=-ln(7/8)=0.1335`

Therefore, the decay constant becomes,

`k=(ln 2)/(t_(1/2))=(0.693)/(5568)=1.24*10^-4 \ "years"^-1`

And so, we get,

`t=0.1335/k=0.1335/(1.24*10^-4 \ "years"^-1)~~1073` years