Question

The age of the Hawaiian islands gets older as you move from east to west. If the half-life of K-40 is 1.3 billion years, approximate the age of Maui if a sample rock on the island has 99.96% of its parent K-40 remaining.​

Answer 1

`t \approx 750550.12\,yr`

Explanation:

The time constant of the isotope is:

`\tau = (1.3* 10^(9)\,yr)/(\ln 2)`

`\tau \approx 1.876 * 10^(9)\,yr`

The decay of the isotope is described by the following model:

`(m)/(m_(o)) = e^{-(t)/(\tau) }`

Now, the time is cleared in the equation:

`t = -\tau \cdot \ln (m)/(m_(o))`

`t = - (1.876* 10^(9)\,yr)\cdot \ln 0.9996`

`t \approx 750550.12\,yr`