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What is the half-life of a radioisotope if 25.0 grams of an original 200gram sample of the isotope remains unchanged after 11.46 days?
Wiki User
∙ 12y ago
Day 0: 200g
Day 50: 100g
Day 100: 50g
Day 150: 25g
Day 200: 12.5g
Day 250: 6.25g
Day 300: 3.125g
Day 350: 1.5625g
Day 400: 0.78125g
Day 450: 0.390625g
Day 500: 0.1953125g
Day 550: 0.09765625g
Day 600: 0.048828125g
So after 600 days you will have about 0.048828125 grams (48.828125 mg) left.
Wiki User
∙ 14y ago
Wiki User
∙ 12y agoThe ratio of mass remaining in going from 800 g to 200 g is 0.25. By inspection, this is two half-lives. Remember that at the first, second, third, and fourth half-life, you have 0.5, 0.25, 0.125, and 0.0625 of the original material left. This means the half life is 2.0 years.
Formally, the equation for half-life is ...
AT = A0 2(-T/H)
... Where A0 is the original activity, AT is the activity after some time T, and H is the half-life in units of T.
Wiki User
∙ 12y agoIf 25 grams remains out of 200 grams, then that is 0.125 of the original mass. By inspection, you can see that this is three half-lives1, so the half-life must be 11.46 / 3, or 3.82 days.
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1One half life is 0.5, two is 0.25, and three is 0.125, as the portion of material remaining.
Wiki User
∙ 11y ago1. 2.87 d
2. 3.82 d
3. 11.46 d
4. 34.38 d
Answer:3.82D
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