Question

The half-life of radium is 1600 years. The fraction of a sample of radium that would remain after 6400 years

Answer 1

The fraction of a sample that would remain after the time $t$ is given by the law of radioactive decay:

$$\dfrac{N}{N_0} = 2^{-\dfrac{t}{T}}$$

Substituting $t = 6400years$ and the half-life $T = 1600years$, obtain:

$$\dfrac{N}{N_0} = 2^{-\dfrac{6400}{1600}} = 0.0625$$

Answer. 0.0625.