Problem Statement: Organochlorine pesticides such as DDT, dieldrin, and lindane

Question

Problem Statement: Organochlorine pesticides such as DDT, dieldrin, and lindane often have a half-life as long as 10 years in the environment. The maximum safe level for lindane is 0.2 ppb. Suppose that an ecosystem has been contaminated at a level of 200 ppb. Estimate how many years it will take for the pesticide to react and diminish to a safe concentration of 0.2 ppb. One way to approach this problem is to count half-lives. It is clear that the pesticide needs to decay to 0.2 ppb. Let's count half-lives until we get that low. Calculate the concentration of lindane after one half-life has passed.

Explanation / Answer

Half life is basically the time taken by the substance to reduce to half of its original composition .

Over here the contaminated level given is 200 ppb. that has to be reduced to 0.2 ppb.

By half life method 200 pb will get reduce to 100 ppb in one half life

100 ppb will get reduced to 50 ppb in second half life

50 ppb will get reduced to 25 ppb in third half life

After nth half life we will have 0.2 ppb .

So we can write

200/(2n) = 0.2

On solving the above equation we get n=9.965,

we will round it up to the nearest integer n=10

Hence, it will take approximately 10 half life for the contaminaton level to get reduced from 200 ppb to 0.2 ppb

After 1 half life the concentration will simply be half that is 200 ppb will become half to 100 ppb

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