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 can start with the given half-life of uranium-235, which is \( 700,000,000 \) years (or \( 7 \times 10^8 \) years), and the additional half-life difference between uranium-238 and uranium-235, which is \( 4.463 \times 10^{11} \) years.

Let's calculate the half-life of uranium-238:

\[ \text{Half-life of uranium-238} = \text{Half-life of uranium-235} + (4.463 \times 10^{11} \text{ years}) \]

Using \( 700,000,000 \) years:

\[ \text{Half-life of uranium-238} = 7 \times 10^8 \text{ years} + 4.463 \times 10^{11} \text{ years} \]

We convert \( 7 \times 10^8 \) years to a form that matches \( 4.463 \times 10^{11} \):

\[ 7 \times 10^8 = 0.0007 \times 10^{11} \]

Now we can add:

\[ \text{Half-life of uranium-238} = 0.0007 \times 10^{11} + 4.463 \times 10^{11} \]

\[ = (0.0007 + 4.463) \times 10^{11} \]

\[ = 4.4637 \times 10^{11} \text{ years} \]

Thus, the half-life of uranium-238 is \( 4.4637 \times 10^{11} \) years.

So the correct answer is:

4.4637×10^11