A sample of rock from the moon is found to contain an exactly equal number of atoms of Uranium and L — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A sample of rock from the moon is found to contain an exactly equal number of atoms of Uranium and Lead. Assuming all the Lead came purely from the decay of Uranium, and given the half-life ($t_{1/2}$) for Uranium is $4.5 \times 10^9\text{ years}$, calculate the age of the rock. Enter your answer as a coefficient $x$, where the age is $x \times 10^9\text{ years}$.
💡 Solution & Explanation
Since the number of Uranium atoms equals the number of Lead atoms, the current number of Uranium atoms $N_U = N_{Pb}$. The original number of Uranium atoms $N_0 = N_U + N_{Pb} = 2N_U$. This implies that exactly half of the initial Uranium atoms have decayed. By definition, the time required for half the substance to decay is one half-life. Thus, the age of the rock is $1 \times t_{1/2} = 4.5 \times 10^9\text{ years}$. The coefficient is $4.5$.