Question

a sample of radioactive material contains 10¹⁸ atoms .the half life of the material is 2000 days.calculate
1.the fraction remaining after 5000 days
2. the activity of the sample after 5000 days

Answer 1

Dear student
$$\begin{gathered} HalflifetimeT=0.693/\lambda \\ \lambda =0.693/2000 \\ N=N_0{e}^{(-\lambda t)N}={{10}^1}^8{e}^{-(0.693/2000)\times 5000)} \\ N={{10}^1}^8{e}^{(-1.7325)} \\ N=1.77\times {10}^{17}atoms \\ andactivity=\lambda N=0.693/2000\times 1.77\times {10}^{17}=6\times 0^{13}atoms/sec \\ Regard \end{gathered}$$