To find the half-life of uranium-238, we can start by understanding the relationship between the two isotopes.
Given that the half-life of uranium-235 is 700,000,000 years, and uranium-238 has a half-life that is 4.463x10^11 years longer, we can use this information to find the half-life of uranium-238.
Let's denote the half-life of uranium-238 as 'x' years. From the given information, we can set up the following equation:
x = 700,000,000 + 4.463x10^11
To solve for 'x', we need to simplify and isolate the variable. Since the half-life of uranium-238 is longer than uranium-235, we know that 'x' would be a larger value.
By rearranging the equation, we get:
4.463x10^11 = x - 700,000,000
Combining like terms, we have:
x - 4.463x10^11 = -700,000,000
Now, isolate 'x' by adding 4.463x10^11 to both sides:
x = 4.463x10^11 - 700,000,000
We can simplify this expression by converting both values to scientific notation. Let's express -700,000,000 as -7x10^8:
x = 4.463x10^11 - 7x10^8
To subtract the values, they first need to have the same exponent. We can rewrite -7x10^8 as -0.7x10^9:
x = 4.463x10^11 - 0.7x10^9
Now, subtract the coefficients:
x = 4.463x10^11 - 0.7x10^9
= 4.463x10^11 - 0.7x10^11
= (4.463 - 0.7)x10^11
= 3.763x10^11
Thus, the half-life of uranium-238 is approximately 3.763x10^11 years in decimal form.