If radio active substance that weight5600grams and half-lifeof 100years is left with 700 grams for how long has the decaying activity been undergoing?

If you have a 120 gram sample of a radioactive element, how many grams of that element will be left after 3 half-lives have passed?

Solution

Given: mass of radioactive sample of an element, number of half-lives

Asked to Solve For: mass of radioactive element after so many half-lives

Solve:

All radioactive samples lose half of their mass after each half-life. Thus, one solution is to calculate the mass after each half-life. (This method only works if you are asked to solve for a whole number of half-lives). Let the passing of time equal to one half-life be represented by and arrow, →. Then the solution is:

120 g → 60 g → 30 g → 15 g

If you want to solve for any number of half-lives, including fractional half-lives, then you use the equation: amount remaining =  (12)n(amountatstart) , where n= number of half-lives. Then the solution is:

amount remaining =  (12)3(120g)=15g

Explanation:

15g

amount remaining (12)3(15)= 15g