When radioactive waste is discussed in the news media, half-lives of waste produ

Question

When radioactive waste is discussed in the news media, half-lives of waste product are often cited in such a way as to give the impression that the longer the half-life, the freater the problems associated with the material. Consider two radioactive materials: A has a half-life of 10 years while B has a half-life of 10000 years.

If equal amounts of both substances are stored in your backyard (or an equivalent, close location), from which would you receive more radiation over your life time? explain.

(please help me explain this problem clearly)

Explanation / Answer

Assuming my lifetime of 100 years.

From A, half-life = 10 years.
Thus, decay during my lifetime = 1 - 0.5^(100/10) = 0.999 or 99.9%

From B, half-life = 100 years.
Thus, decay during my lifetime = 1 - 0.5^(100/100) = 0.50 or 50%

Thus, radiation through A will be much higher than B.

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