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If 18 g of a radioactive substance are present initially and 9 yr later only 9 g remain, how much of the substance will be present after 12 yr?

After 12 yr there will be g of a radioactive substance.
(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as needed.)

User Kartika
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Final answer:

To find the amount of radioactive substance remaining after 12 years, we calculate the decay over the additional 3 years as a fraction of the known half-life, which results in approximately 7.143 g of the substance remaining.

Step-by-step explanation:

When dealing with radioactive decay, the amount of a radioactive substance remaining after a certain period can be calculated using the concept of half-life. In this case, since the half-life is 9 years (given that half of the substance decayed from 18 g to 9 g in 9 years), we need to calculate how much will remain after an additional 3 years, making it a total of 12 years.

We can determine the amount remaining after an additional 3 years by realizing that this period constitutes one-third of a half-life. Therefore, the amount does not halve, but decreases according to the exponential decay rule.

Amount remaining after 9 years (one half-life) = 1/2 of the initial amount = 9 g

After 12 years, we can apply the formula: Remaining amount = initial amount * (1/2)^(time elapsed/half-life)

Thus, Remaining amount after 12 years = 9 g * (1/2)^(3/9) = 9 g * (1/2)^(1/3)

To find (1/2)^(1/3), we calculate the cube root of 1/2 which is approximately 0.7937.

Therefore, Remaining amount after 12 years = 9 g * 0.7937 ≈ 7.143 g (rounded to three decimal places)

User Kfuglsang
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Answer:

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Step-by-step explanation:

User Jyothish
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