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

Answer:

$t \approx 750550.12\,yr$

Step-by-step explanation:

The time constant of the isotope is:

$\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}$

$\tau \approx 1.876 \times 10^{9}\,yr$

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

$\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }$

Now, the time is cleared in the equation:

$t = -\tau \cdot \ln \frac{m}{m_{o}}$

$t = - (1.876\times 10^{9}\,yr)\cdot \ln 0.9996$

$t \approx 750550.12\,yr$