Answer :

If the half-life of radium-226 is 1620 years. The for 55% decomposition of its original amount will take 1397 years.

Calculate the half-life by using the formula as,

A(t) = I(0.5)^t/t1/2

Where t1/2 = half life = 1620

Final amount, A(t) = 0.55 of its original amount = 0.55I

Hence, we have

0.55I = I(0.5)^t/1620

Taking the log of both sides we get,

log(0.55) = log(0.5)^t/1620

t/1620 = log(0.55) / log(0.5)

t/1620 = 0.8624964

t = 0.8624964 × 1620

t = 1397.2441

t = 1397 (nearest whole number)

Hence, for 55% decomposition of its original amount will take 1397 years.

Learn more about half life from the link given below.

https://brainly.com/question/14883322

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