Question

The half-life of the uranium isotope 235 U is 700 million years. The earth is approximately 4.5 billion years old. How much more 235 U was there when the earth formed than there is today? Give your answer as the then-to-now ratio

Short answer

The number of uranium atoms present on the Earth today is equal to the number of uranium atoms present on the Earth when it was born and${\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$t2$}\right.}$

Step-by-step solution

Atoms present on the earth

${\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$t2$}\right.}$N_u=(N_u)₀

Here, N is the number of uranium atoms present on the Earth today, U is the number of uranium atoms present on the Earth when it was bom, is the age of the Earth and is the half-life of the uranium.

Rearrange the expression as the ratio of and N.