Physical application: Radioactive decay

Physical application: Radioactive decay
Example : The rate of decomposition of radium is proportional to the amount present at any time. The half-life of radioactive radium is 1600 years . If a sample initially contains 50 gm, how long will it be until it contains 45 gm ?
Solution: Let be the amount of radium present at time in years.


Physical application: Radioactive decay
Example : The rate of decomposition of radium is proportional to the amount present at any time. The half-life of radioactive radium is 1600 years . If a sample initially contains 50 gm, how long will it be until it contains 45 gm ?
Solution: Let be the amount of radium present at time in years.





We have
Thus
The half-life of radium is 1600 years it s meaning that






H.W (1) The rate of decomposition of radioactive einsteinium is proportional to the amount present at any time. The half-life of radioactive einsteinium is 276 days . After 100 days, 0.5 gram remains. What was the initial amount?
(2) The rate of decomposition of radioactive einsteinium is proportional to the amount
present at any time. The half-life of radioactive radium is 1600 years. If a sample initially contains 30 grams, how much the amount will remain after 250 years?



We have
Thus
The half-life of radium is 1600 years it s meaning that






H.W (1) The rate of decomposition of radioactive einsteinium is proportional to the amount present at any time. The half-life of radioactive einsteinium is 276 days . After 100 days, 0.5 gram remains. What was the initial amount?
(2) The rate of decomposition of radioactive einsteinium is proportional to the amount
present at any time. The half-life of radioactive radium is 1600 years. If a sample initially contains 30 grams, how much the amount will remain after 250 years?