The half-life of uranium-235 is 700,000,000 years. The half-life of uranium-238 is 4.463 x 10^11 years longer. What is the half-life of uranium-238? The answer should be in decimal form.
a 516,300,000,000
b 4.4637 x 10^11
c 447,000,000,000
d 11,463,000,000
To find the half-life of uranium-238, we add the additional time to the half-life of uranium-235.
The half-life of uranium-238 = 700,000,000 + (4.463 x 10^11) = 4.4635163 x 10^11 years.
Therefore, the half-life of uranium-238 is approximately 4.4635163 x 10^11 years.
Answer: b) 4.4637 x 10^11
To find the half-life of uranium-238, we need to calculate the difference in half-life between uranium-238 and uranium-235.
Given:
Half-life of uranium-235 = 700,000,000 years
The half-life of uranium-238 is 4.463 x 10^11 years longer than that of uranium-235.
To calculate the half-life of uranium-238, we add the difference in half-life to the half-life of uranium-235.
Half-life of uranium-238 = Half-life of uranium-235 + Difference in half-life
Half-life of uranium-238 = 700,000,000 years + 4.463 x 10^11 years
To simplify the answer, we convert 4.463 x 10^11 years to decimal form:
4.463 x 10^11 years = 446,300,000,000 years
Now, we can calculate the half-life of uranium-238:
Half-life of uranium-238 = 700,000,000 years + 446,300,000,000 years
Half-life of uranium-238 = 447,000,000,000 years
Therefore, the half-life of uranium-238 is 447,000,000,000 years, which is equivalent to option (c).
To find the half-life of uranium-238, we need to calculate the difference in half-lives between uranium-235 and uranium-238.
Given that the half-life of uranium-235 is 700,000,000 years, and the half-life of uranium-238 is 4.463 x 10^11 years longer, we can calculate the half-life of uranium-238 by adding the difference to the half-life of uranium-235.
Difference in half-lives = 4.463 x 10^11 years
Half-life of uranium-238 = Half-life of uranium-235 + Difference in half-lives
Substituting the values we have:
Half-life of uranium-238 = 700,000,000 years + 4.463 x 10^11 years
Now, we add the numbers:
Half-life of uranium-238 ≈ 4.463 x 10^11 years
Therefore, the answer is in the form b) 4.4637 x 10^11.