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

1 Answer
Nam D.
Mar 19, 2018

#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

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