The half-life of uranium-235 is 700,000,000 years. The half-life of uranium-238 is 4.463×1011 years longer. What is the half-life of uranium-238? The answer should be in decimal form.(1 point)

Question

Responses

4.4637×1011
4.4637 times 10 superscript 11 baseline

11,463,000,000
11,463,000,000

447,000,000,000
447,000,000,000

516,300,000,000

Answer 1

To find the half-life of uranium-238, we need to add the half-life of uranium-235 to the additional time given:

1. The half-life of uranium-235 is \( 700,000,000 \) years.
2. The half-life of uranium-238 is \( 4.463 \times 10^{11} \) years longer than that of uranium-235.

First, we convert \( 4.463 \times 10^{11} \) years into decimal form:

\[ 4.463 \times 10^{11} = 446,300,000,000 \text{ years} \]

Now we can calculate the half-life of uranium-238:

\[ \text{Half-life of } uranium-238 = 700,000,000 + 446,300,000,000 \]

This equals:

\[ 700,000,000 + 446,300,000,000 = 447,000,000,000 \text{ years} \]

Therefore, the half-life of uranium-238 is

\[ \boxed{447,000,000,000} \]

So the correct response is \( 447,000,000,000 \).