Question #282258

9. Chemical analysis shows that a bone fragment contains 10 g of C. Its activity is 50


counts/min. How old is the bone fragment?

1
Expert's answer
2021-12-27T13:04:01-0500

N=mNAM=106.02102312=51023,N=\frac{mN_A}M=\frac{10\cdot 6.02\cdot 10^{23}}{12}=5\cdot 10^{23},

N0=Nη=510231.31012=6.51011,N_0=N\eta =5\cdot 10^{23} \cdot1.3\cdot10^{-12} = 6.5\cdot10^{11},

A0=N0λ=6.510110.695730365243600=2.53 s1,A_0=N_0\lambda = \frac{6.5\cdot10^{11 }\cdot 0.69 }{5730 \cdot 365 \cdot 24 \cdot 3600 }= 2.53~ s^{-1},

A=A0eλt,    A=A_0e^{-\lambda t},\implies

λt=lnA0A=ln2.536050=1.11,\lambda t=\ln \frac{A_0}A=\ln \frac{2.53\cdot 60}{50}=1.11,

t=1.11λ=1.1153700.69=9180 years.t=\frac {1.11}{\lambda}=\frac{1.11\cdot 5370}{0.69}=9180~\text{years}.


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