Answer to Question #120118 in Electricity and Magnetism for Higgins

Question

Analysis of a rock sample shows that only 1/16 of the original amount of chlorine-36 remains in
the rock. Estimate the age of the rock given that the half-life of chlorine-36 is 3.0 x 105
a

Answer 1

The number of atoms N remaining after time t is given by the law od radioactive decay:

$$N = N_02^{-\frac{t}{T}}$$

where $N_0$ is the number of atoms at the initial moment of time, $T$ is the half-life.

Expressing $t$ (age) from this equation:

$$t = T\log_2\dfrac{N_0}{N}$$

As far as $N/N_0 = 1/16$ and $T = 3\cdot 10^{5} years$, obtain:

$$t = 3\cdot 10^{5}\log_216 = 3\cdot 10^{5}\cdot 4 = 1.2\cdot 10^6years$$

Answer. The age of the sample is 1.2*10^6 years.