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Answer :
Final answer:
It will take 2.1 billion years for 600 kg of Uranium-235 to decay to 75 kg, as it requires 3 half-lives, and each half-life of Uranium-235 is 700 million years.
Explanation:
To find out how long it will take to decay from 600 kg of Uranium-235 to 75 kg, we can use the concept of half-lives. A half-life is the time required for half of the radioactive nuclei in a sample to undergo radioactive decay. In this case, Uranium-235 has a half-life of 700 million years.
Let's calculate the number of half-lives required to reduce 600 kg to 75 kg:
- First half-life: 600 kg to 300 kg.
- Second half-life: 300 kg to 150 kg.
- Third half-life: 150 kg to 75 kg.
So, it takes 3 half-lives for 600 kg to decay to 75 kg.
Now, we can calculate the total time:
- 3 half-lives × 700 million years per half-life = 2100 million years.
To express this in billion years:
- 2100 million years ÷ 1000 = 2.1 billion years.
It will take 2.1 billion years for 600 kg of Uranium-235 to decay to 75 kg.
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Rewritten by : Barada
It will take 2.1 billion years for 600kg of Uranium-235 to decay to 75kg, using the concept of half-life which involves reductions by half every 700 million years.
Calculating the Decay Time for Uranium-235
To determine how long it will take for 600kg of Uranium-235 to decay to 75kg, we use the concept of half-life. The half-life of Uranium-235 is 700 million years.
First, we calculate the number of half-lives needed to reduce the amount of Uranium-235 from 600kg to 75kg.
Since 75kg is 1/8th of 600kg, we need to find when the amount will be 1/8th of the original:
1 half-life = 600kg to 300kg (1/2)
2 half-lives = 300kg to 150kg (1/4)
3 half-lives = 150kg to 75kg (1/8)
This means it takes 3 half-lives to reach 75kg from 600kg.
Each half-life is 700 million years, so:
3 half-lives × 700 million years = 2.1 billion years
Hence, it will take 2.1 billion years for 600kg of Uranium-235 to decay to 75kg.
