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The half-life of radium is 1600 years. What is the fraction of sample undecayed after 6400 years?
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$\frac{1}{16}$
Half-life, $T=1600$ years Time of decay, $t=6400$ years Number of half-lives, $n=\frac{t}{T}=\frac{6400}{1600}=4$ Fraction undecayed $=\frac{N}{N_0}=\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^4=\frac{1}{16}$
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