Question

Alexander Litvinenko was poisoned with 10 micrograms of the radioactive substance Polonium-210. Since radioactive decay follows a compounded continuously model, we can determine the amount of substance left in Alexander Litvinenko's body at any given time. If Polonium-210 has a decay rate of .502%, then determine the amount of Polonium-210 left in his body after 190 days. Provide 3 decimal places and units in your answer.

Answer 1

We have

Initial mass of Polonium-210

`N_0=10\text{ micrograms}`

Decay rate, r = 0.502% = 0.00502

Time, t = 190 days

Then, We know that left amount is given by

`N=N_0e^(-rt)`

Solving

`N=10e^(-0.00502(190))=10e^(-0.9538)=3.853`

Answer: 3.853 micrograms