Question

If you find an igneous rock which has 450 radioactive isotopes and 3,150 stable daughter isotopes, how many half-lifes of this isotope have passed since this rock first formed?

Answer 1

Answer:

$3t_{1/2}$  

Explanation:

To find the half-lifes of the isotope we need to use the following equation:

$N_{t} = N_{0}2^{-\frac{t}{t_{1/2}}}$     (1)

where Nt: is the amount of the isotope that has not yet decayed after a time t, N₀: is the initial amount of the isotope, t: is the time and $t_{1/2}$: is the half-lifes.

By solving equation (1) for t we have:

$\frac{t}{t_{1/2}} = - \frac{Ln(Nt/N_{0})}{Ln(2)}$

Having that:

Nt = 450

N₀ = 3150 + 450 = 3600,

The half-lifes of the isotope is:

$t = - \frac{Ln(450/3600)}{Ln(2)} \cdot t_{1/2} = 3t_{1/2}$

Therefore, 3 half-lives of the isotope passed since the rock was formed.

I hope it helps you!