Question #194778

The 614𝐶 isotope has a half-life of 5730 yr. If at some time a sample contains 1.00 x 1022 carbon-14 nuclei, what is the activity of the sample? 


1
Expert's answer
2021-05-18T11:09:59-0400

Given

Number of nuclei is N=1.00×1022N= 1.00\times 10^{22}

Half life is T1/2=5730year=1.807×1011secondsT_{1/2}=5730 year=1.807 \times 10^{11} seconds

The activity of the sample is

R=λN=ln2t1/2N=ln21.807×1011seconds(1.00×1022)R=\lambda N =\frac{ln2}{t_{1/2}}N =\frac{ln2}{1.807 \times 10^{11} seconds}( 1.00\times 10^{22} )

=3.836×1010decay/s=3.836\times 10^{10} decay/s


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