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The half-life of a substance is million years. If a certain amount is only considered safe when its radioactivity has dropped to of the original level, approximately how much time must the substance be stored securely to be safe? billion years million years million years billion years
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Q. The half-life of a substance is million years. If a certain amount is only considered safe when its radioactivity has dropped to of the original level, approximately how much time must the substance be stored securely to be safe? billion years million years million years billion years
- Determine Half-Lives: We need to determine how many half-lives it takes for a substance to reach of its original radioactivity level. is equivalent to , which simplifies to . This means the substance needs to go through enough half-lives to be th of its original amount.
- Express as Power: To find out how many half-lives it takes to reach th of the original amount, we can express as a power of , since each half-life reduces the substance by half. is the same as , because . This means it takes half-lives to reach of the original radioactivity level.
- Calculate Total Time: Now that we know it takes half-lives to reach of the original radioactivity, we can calculate the total time by multiplying the number of half-lives by the duration of one half-life.The half-life is given as million years, so we multiply half-lives by million years per half-life. million years million years.
