Question

A radioactive isotope has a half-life of 5,000 years. A rock originally contained 16 grams of radioactive isotope, and now contains 4 grams. Approximately how many years old is the rock?

Answer 1

Answer:

10,000 years

Explanation:

Given that,

Half life of the radioactive isotope, $t_{\frac{1}{2}}$ = 5000 years

Initial composition, $N_0$ = 16 grams

Final composition, $N$ = 4 grams

We know that,

$N=N_0\times (\dfrac{1}{2})^\frac{t}{t_\frac{1}{2}}}\\\\4=16(0.5)^\frac{t}{5000}}\\\\\dfrac{4}{16}=(0.5)^{\frac{t}{5000}}\\\\0.25=(0.5)^\frac{t}{5000}\\\\0.5^2=(0.5)^\frac{t}{5000}\\\\2=\dfrac{t}{5000}\\\\t=2\times 5000\\\\t=10000\ yrs$

Therefore, the age of the rock is 10,000 years.