The half-life of uranium-235 is 700,000,000 years. The half-life of uranium is 4.463 x 10^11 years longer. What is the half-life of uranium-238? The answer should be in decimal form.
1. 11,463,000,000
2. 516,300,000,000
3. 4.4637 x 10^11
4. 447,000,000,000
To find the half-life of uranium-238, we need to add the additional time of 4.463 x 10^11 years to the half-life of uranium-235, which is 700,000,000 years.
The sum of the two half-lives is 700,000,000 + 4.463 x 10^11.
Converting the scientific notation to decimal form, we have:
4.463 x 10^11 = 4463 x 10^8 = 4463 x 100,000,000 = 4463 x 10^8
Adding this to 700,000,000:
700,000,000 + 4463 x 10^8 = 700,000,000 + 4463 x 100,000,000 = 700,000,000 + 446,300,000,000.
Therefore, the half-life of uranium-238 is 446,300,000,000 years.
So, the correct answer is 4. 447,000,000,000.
To find the half-life of uranium-238, we can subtract the half-life of uranium-235 from the half-life of uranium:
Half-life of uranium-238 = Half-life of uranium - Half-life of uranium-235
Substituting the values given:
Half-life of uranium-238 = 4.463 x 10^11 years - 700,000,000 years
Simplifying:
Half-life of uranium-238 ≈ 4.463 x 10^11 years - 7 x 10^8 years
Since the exponents are the same, we can subtract the coefficients:
Half-life of uranium-238 ≈ 4.4563 x 10^11 years
So, the answer is option 3: 4.4637 x 10^11.
To find the half-life of uranium-238, you can start by knowing that it is 4.463 x 10^11 years longer than the half-life of uranium-235, which is 700,000,000 years.
To determine the half-life of uranium-238, you can add the difference in half-lives to the half-life of uranium-235.
The difference between the half-lives is obtained by subtracting the half-life of uranium-235 from the half-life of uranium-238:
4.463 x 10^11 years - 700,000,000 years = 4.463 x 10^11 years
Therefore, the half-life of uranium-238 is 4.463 x 10^11 years. Option 3 is the correct answer.