Carbon-14 has a half-life of 5,730 years. In how many years will 120 grams of Carbon-14 decay to 15 grams?

A. 11,460 years

B .17,190 years

C. 22, 920 years

D. 28,650 years

Question

Carbon-14 has a half-life of 5,730 years. In how many years will 120 grams of Carbon-14 decay to 15 grams? 

 A. 11,460 years

B .17,190 years

C. 22, 920 years

D. 28,650 years

anonymous · Answer

the radioactive decay equation:
$$N(t)=N_0e^{-t/\tau}\
\implies {N\over N_0}=e^{-t/\tau}\
\ln\left(N\over N_0\right)={-t\over \tau}\
t = \tau \ln\left(N_0\over N\right)\
\;\
N=15\,{\rm g}\
N_0=120\,{\rm g}\
\tau=5730\
t=?
$$