the half life of Uranium -238 is 4.5 billion years and the age of earth is 4.5 X 109 years. What fraction of Uranium-238 that was present when earth was formed still remains?
4.5x10^9 = 4.5 billion years.
so, one half-life has passed...
Well, let me put on my little clown nose and calculate that for you! So, if the half-life of Uranium-238 is 4.5 billion years and the age of the Earth is also 4.5 billion years, we can assume that approximately half of the Uranium-238 has decayed over this time.
Therefore, only half of the original Uranium-238 that was present when Earth was formed still remains. So, to answer your question, the fraction of Uranium-238 that is left is 1/2, or in more scientific terms, 0.5.
But hey, don't worry, Earth is still rockin' it with the remaining Uranium-238!
To determine the fraction of Uranium-238 that remains since the formation of Earth, we can use the concept of half-life.
1. Calculate the number of half-lives that have passed since the formation of the Earth:
Number of half-lives = (Age of Earth)/(Half-life of Uranium-238)
Number of half-lives = (4.5 X 10^9 years)/(4.5 billion years)
= 1
This means that one half-life of Uranium-238 has passed since the formation of the Earth.
2. Knowing that one half-life has passed, we can determine the fraction remaining:
Fraction remaining = (1/2)^1 (The exponent corresponds to the number of half-lives)
Thus, the fraction of Uranium-238 that remains since the formation of the Earth is 1/2 or 0.5.