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.
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