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A substance has a half-life of 2.041 minutes. If the initial amount of the substance was 118.4 grams, how many half-lives will have passed before the substance decays to 7.4 grams?

User Aryan G
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1 Answer

5 votes

Final answer:

It will take 4 half-lives for the substance to decay from 118.4 grams to 7.4 grams.

Step-by-step explanation:

To determine the number of half-lives that will have passed before the substance decays to 7.4 grams, we need to calculate the number of half-lives it takes for the initial amount to decay to that level.

First, let's calculate the number of half-lives it takes for the initial amount of 118.4 grams to decay to 7.4 grams. Each half-life reduces the amount by half, so we need to divide 118.4 grams by 2.

118.4 grams ÷ 2 = 59.2 grams

Since 59.2 grams is still greater than 7.4 grams, we need to continue dividing by 2.

59.2 grams ÷ 2 = 29.6 grams

29.6 grams ÷ 2 = 14.8 grams

14.8 grams ÷ 2 = 7.4 grams

It took 4 half-lives for the initial amount of 118.4 grams to decay to 7.4 grams. Therefore, 4 half-lives will have passed before the substance decays to 7.4 grams.

User Ashish Rajput
by
8.3k points
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