The isotype caesium -137, which has a half life of 30 years, is a product of nuclear power plants. How long will it take for the amount of this isotype in a sample of caesium to decay to one-sixteenth of its original amount?
first half life 1/2
second 1/4
third 1/8
fourth 1/16
so how long is four half-lives?
120 years
30=1/2
60=1/4
90=1/8
120=1/16
try the equation No= 1/2^n
To determine how long it will take for the amount of caesium-137 to decay to one-sixteenth of its original amount, you need to calculate the number of half-lives it will take to reach that point.
In this case, one-half of the isotope decays in 30 years, so we need to find how many times 30 years goes into the total time it takes for the isotope to decay by one-sixteenth (1/16) of its original amount.
Since each half-life represents a reduction by a factor of 1/2, 1/16 can be achieved by taking four successive half-lives.
So, to find the total time it takes, you multiply the half-life (30 years) by the number of half-lives (4):
30 years/half-life * 4 half-lives = 120 years
Therefore, it will take 120 years for the amount of caesium-137 isotope to decay to one-sixteenth of its original amount.