Question

A radioactive nucleus has a half-life of 5*108 years. Assuming that a sample of rock (say, in an asteroid) solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today? The age of the solar system is 4.5*109 years. (No calculator is necessary, but if it helps use it.)

Answer 1

Answer:

0.002

Explanation:

The half-life of the radioactive nucleus is related to its quantity, by the following equation:

$N_{t} = N_{0}2^{-t/t_{1/2}}$

Where:

N(t): is the quantity of the radioactive nucleus at time t

N₀: is the  initial quantity of the radioactive nucleus

t: is the time = 4.5x10⁹ years

t(1/2): is the half-life of the radioactive nucleus = 5x10⁸ years

$\frac{N_{t}}{N_{0}} = 2^{-4.5 \cdot 10^{9} y/5 \cdot 10^{8} y} = 2 \cdot 10^{-3}$

Therefore, the fraction of the radioactive element in the rock today is 0.002.

I hope it helps you!