The half-life of radium is 1600 years. If the initial amount is

From the formula q(t) = q_{0} 2^{kt }and the definition of half-life T, q_{0}/2 = q_{0}2^{kT }. Then 2^{kT }= ½ = 2^{–1} and kT = –1. Finally, k = –1/T = –1/1600 = –6.25×10^{–4} .

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