An original sample of K-40 has a mass of 25.00 grams. After $3.9 xx 10^9$ years, 3.125 grams of the original sample remains unchanged. What is the half-life of K-40?

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Answer 1 · 2017-06-21T22:19:13

$1.3xx10^9 yrs$

From $C_"final" = C_"initial"e^(-kt)$ solve for rate constant (k) ...

=> $k = (ln(C_f/C_i)/-t)$ = $ln(3.125/25)/(-3.9xx10^9)$ = $5.33xx10^-10 yrs^-1$

Use the rate constant (k) in the half-life equation ...

=> $t_(1/2) = (0.693/k) = (0.693/(5.33xx10^-10))years$ $1.3xx10^9 years$

An original sample of K-40 has a mass of 25.00 grams. After 3.9 xx 10^93.9 xx 10^9 years, 3.125 grams of the original sample remains unchanged. What is the half-life of K-40?