Finding original amount in half-life problem
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Since
$$\text{Amount remaining} =\text{Original Amount} \times \bigg(\frac{1}{2}\bigg)^{\text{number of half lives}} $$
solve for $X$ in the equation
$$10 = X \times \bigg(\frac{1}{2}\bigg)^{\frac{1000}{1590}}$$
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jaykirby
Updated on August 01, 2022Comments
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jaykirby over 1 year
Say the half-life of an element is 1590 years. If 10g of the element is left after 1000 years, how much was there originally?
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Gerry Myerson over 10 yearsWhat do you know about this kind of problem? Have you not been shown some formulas that might be useful?
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jaykirby over 10 yearsI know how to calculate half-life but don't know how to find the original amount.
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Gerry Myerson over 10 yearsSo, how do you calculate half-life?
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jaykirby over 10 yearsln(fraction remaining) = -kt
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Gerry Myerson over 10 yearsWhat does $k$ stand for? what does $t$ stand for? How would you use that formula? what would you have to know, and what computation would you do? Full sentences, please.
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jaykirby over 10 yearsk stands for rate constant and t for time. to use the formula you would need to know at least 2 of the 3 unknowns.
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Angela Pretorius over 10 yearsThe amount of the element has halved $\frac{1000}{1590}$ times. There was $\displaystyle 2^{\frac{1000}{1590}}\times 10g$ initially.
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