Question

A sample of rock from moon contains equal number of atoms of uranium and lead. $t_{1 / 2}$ for $U =4.5 \times 10^{9}$ years. The age of the rock would be :

• A. $2.25\times 10^{9}$ years
• B. $13.5\times 10^{9}$ years
• C. $9.0\times 10^{9}$ years
• D. $4.5\times 10^{9}$ years

Answer 1

Answer: (D)

$4.5\times 10^{9}$ years

Answer 2

One atom of ${ }_{92} U ^{238}$ produces one atom of ${ }_{82} Pb ^{206}$ on decay. Therefore, the number of atom of $U ^{238}$ and $Pb ^{206}$ in a rock sample is equal only when half of the number of $U ^{238}$ originally present decay to give same number of $Pb ^{206}$. Thus the time elapsed will be equal to the half-life period of $U ^{238}$