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?
Given
Number of nuclei is N=1.00×1022N= 1.00\times 10^{22}N=1.00×1022
Half life is T1/2=5730year=1.807×1011secondsT_{1/2}=5730 year=1.807 \times 10^{11} secondsT1/2=5730year=1.807×1011seconds
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} )R=λN=t1/2ln2N=1.807×1011secondsln2(1.00×1022)
=3.836×1010decay/s=3.836\times 10^{10} decay/s=3.836×1010decay/s
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