High School

The half-life of copper-67 \((^{67}\text{Cu})\) is 62 hours. If it takes 210 hours to ship 40 pounds across the country, how much will be left when it arrives?

Answer :

Final answer:

Approximately 10.33% of the original amount of copper-67 will be left.

Explanation:

The half-life of copper-67 (67Cu) is 62 hours. The question asks about the amount of copper-67 that will be left when it arrives after a shipping time of 210 hours. To calculate this, we can use the concept of half-life and exponential decay. The number of half-lives that occur during the shipping time can be determined by dividing the total shipping time by the half-life, which gives us 210 hours / 62 hours = 3.387. Since the half-life represents the time it takes for half of the substance to decay, after 3.387 half-lives, approximately 50% * (1/2)^3.387 = 10.33% of the original amount of copper-67 will be left.

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