Determine the total time required for an 80.0-gram sampleof i-131 to decay until only 1.25 grams of the sample remains unchanged.

481.2 days

Initial mass of I-131  is 80.0 gram

Remaining mass of I-131 after decay is 1.25 grams

We are required to determine the time taken for it to decay;

The half-life of I-131 is 80.2 days

But;

Remaining mass = Initial mass × (1/2)^n , where n is the number of half lives

Therefore;

1.25 g = 80.0 g × 0.5^n

0.015625 = 0.5^n

n = log 0.015625 ÷  log 0.5

  = 6 half lives

But, Time = half life × number of half lives

                = 6 × 80.2 days

                = 481.2 days

Therefore, it will take 481.2 days for a mass of 80.0 g I-131 to decay to 1.25 g.

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