Question

The number of U${}^{238}$ nuclei in a rock sample is equal to the number of Pb${}^{206}$ atoms. The half-life of U${}^{238}$ is 4.5 x ${10}^9$ years.The age of the rock is

• A. 4.5 x10${}^{9}y$
• B. 9x10${}^{9}y$
• C. 13.5x10${}^{9}y$
• D. 18x10${}^{9}y$

Answer 1

The correct option is A 4.5 x10${}^{9}y$

As, $U^{238}$ disintegrates to form $P{b}^{206}$ atoms, the ratio of $U^{238}:P{b}^{206}$ is $1:1$, i.e., 1 half life has been over as half of $U^{238}$ has decayed to form same amount of $P{b}^{206}.$

Thus the age of rock is 1 half life i.e., $4.5\times {10}^{9}years$