A sample of rock moon contains equal numbers of atoms of uranium and lead `t_(1//2)` for `U` is `4.5 xx 10^(9)` years. The age of rock would be
a. `4.5 xx 10^(9)` years b. `9.0 xx 10^(9)` years
c. `13.5 xx 10^(9)` years d. `2.25 xx 10^(9)` years

Explanation

To determine the age of the rock sample that contains equal numbers of uranium and lead atoms, we can use the principles of radioactive decay and the half-life of uranium. Here’s a step-by-step solution:

### Step 1: Understand the relationship between uranium and lead
Since the rock contains equal numbers of uranium (U) and lead (Pb) atoms, we can denote the number of uranium atoms as \( N_U \) and the number of lead atoms as \( N_P \). Given that \( N_U = N_P \), we can say that if there are \( x \) atoms of uranium, there are also \( x \) atoms of lead.

### Step 2: Use the half-life of uranium
The half-life \( t_{1/2} \) of uranium is given as \( 4.5 \times 10^9 \) years. This means that every \( 4.5 \times 10^9 \) years, half of the uranium will decay into lead.

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