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

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Solution

## Dear student $HalflifetimeT=0.693/\lambda \phantom{\rule{0ex}{0ex}}\lambda =0.693/2000\phantom{\rule{0ex}{0ex}}N={N}_{0}{e}^{\left(-\lambda t\right)N}={{10}^{1}}^{8}{e}^{-\left(0.693/2000\right)×5000\right)}\phantom{\rule{0ex}{0ex}}N={{10}^{1}}^{8}{e}^{\left(-1.7325\right)}\phantom{\rule{0ex}{0ex}}N=1.77×{10}^{17}atoms\phantom{\rule{0ex}{0ex}}andactivity=\lambda N=0.693/2000×1.77×{10}^{17}=6×{0}^{13}atoms/sec\phantom{\rule{0ex}{0ex}}Regard$

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