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. Carbon has a half-life of years. After , years, only remains. What was the mass of the original sample?
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Q. . Carbon has a half-life of years. After , years, only remains. What was the mass of the original sample?
- Determine Initial Mass: We need to determine the initial mass of a Carbon- sample that has decayed to after years. The half-life of Carbon- is years. We can use the formula for exponential decay to find the original mass.
- Calculate Number of Half-Lives: First, let's determine how many half-lives have passed in years. We do this by dividing the total time by the half-life of Carbon.Number of half-lives = Total time / Half-life = years / years
- Calculate Remaining Mass: Calculating the number of half-lives:Number of half-lives = This means that the Carbon sample has gone through half-lives.
- Calculate Initial Mass: Now, we can use the fact that after each half-life, the mass of the radioactive substance is halved. After half-lives, the mass would be halved times.Initial mass = Remaining mass
- Final Calculation: Calculating the initial mass:Initial mass =
- Final Calculation: Calculating the initial mass:Initial mass = Final calculation of the initial mass:Initial mass = The original mass of the Carbon sample was grams.
