Answer to Question #194778 in Atomic and Nuclear Physics for Tia Brown

Question

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? 

Answer 1

Given

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

Half life is $T_{1/2}=5730 year=1.807 \times 10^{11} seconds$

The activity of the sample is

$R=\lambda N =\frac{ln2}{t_{1/2}}N =\frac{ln2}{1.807 \times 10^{11} seconds}( 1.00\times 10^{22} )$

$=3.836\times 10^{10} decay/s$