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Q.

The half-life of a radioactive substance is 5000 years. In how many years, its activity will decay to 0.2 times of its initial value ? Given log105 = 0.6990.

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An Intiative by Sri Chaitanya

a

1.16 × 105 years

b

1.16 × 104 years

c

1.16 × 103 years

d

1.16 × 106 years

answer is B.

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Detailed Solution

T = 5000 yrs
A0A=2t/T=A00.2A0=2t/5000⇒5=2t/5000
Taking log on both sides
⇒log105=t5000log102;0.699=t5000(0.3010)t=0.699×50000.3010=1.16×104yrs

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