the half-life on uranium-235 is 700,000,000 years. the half-life of uranium-238 is 4.463x10^11 years longer. what is the half-life of uranium-238? the answer should be in decimal form
To find the half-life of uranium-238, we need to add the additional time to the half-life of uranium-235.
Half-life of uranium-235 = 700,000,000 years
Additional time for uranium-238 = 4.463 x 10^11 years
The half-life of uranium-238 = 700,000,000 + 4.463 x 10^11
= 446,300,000,000 years
So, the half-life of uranium-238 is approximately 446,300,000,000 years in decimal form.
To find the half-life of uranium-238, we need to determine the difference in half-lives between uranium-235 and uranium-238.
The half-life of uranium-235 is given as 700,000,000 years.
To find the half-life of uranium-238, we add the difference in half-lives between the two isotopes:
700,000,000 + 4.463x10^11 = 4.463x10^11 + 7.000x10^8
Simplifying this expression:
4.463x10^11 + 7.000x10^8 = 4.463x10^11 + 0.7x10^9
Now, we add the exponents and multiply the coefficients:
4.463x10^11 + 0.7x10^9 = 4.463x10^11 + 0.7x10^2 (shifting the decimal point 9 places to the left)
4.463x10^11 + 0.7x10^2 = 4.463x10^11 + 0.07
When we combine like terms:
4.463x10^11 + 0.07 = 4.463x10^11
Therefore, the half-life of uranium-238 is 4.463x10^11 years.
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.