To find the half-life of uranium-238, we start with the half-life of uranium-235, which is 700,000,000 years. The problem states that the half-life of uranium-238 is 4.463 × 10^11 years longer than that of uranium-235.
First, we'll convert \(4.463 \times 10^{11}\) years to decimal form: \[ 4.463 \times 10^{11} = 446,300,000,000 (approximately) \]
Now, we can calculate the half-life of uranium-238: \[ \text{Half-life of uranium-238} = \text{Half-life of uranium-235} + 4.463 \times 10^{11} \] \[ = 700,000,000 + 446,300,000,000 \] \[ = 447,000,000,000 \]
Thus, the half-life of uranium-238 is \(447,000,000,000\) years.
Final Answer: 447,000,000,000