Question

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?

Answer 1

`1.3xx10^9 yrs`

Explanation:

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`