Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately 12 years. That is, every 12 years, the amount of tritium decreases by 50%. If a new tritium EXIT sign contains 25 curies of tritium, approximately how many curies of tritium will remain after 24 years? Choose 1 answer: (A) 6.25 curies (B) 12.5 curies (C) 25 curies (D) 30 curies

Question

Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately 12 years. That is, every 12 years, the amount of tritium decreases by  50%. If a new tritium EXIT sign contains 25 curies of tritium, approximately how many curies of tritium will remain after 24 years? Choose 1 answer: (A) 6.25 curies (B)  12.5 curies (C)  25 curies (D) 30 curies

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Identify Values: Identify the values of the initial amount (a), total time (t), and half-life period (h). Initial amount (a) = 25 curies Total time (t) = 24 years Half-life period (h) = 12 yearsUse Half-life Formula: Use the half-life formula to calculate the remaining amount of tritium after 24 years. The formula is y = a * (1/2)^(t/h), where y is the remaining amount after time t, a is the initial amount, and h is the half-life period.Substitute Values: Substitute the values into the formula. y = 25 * (1/2)^(24/12)Simplify Exponent: Simplify the exponent in the formula. 24/12 = 2, so the exponent becomes (1/2)^2.Calculate Remaining Quantity: Calculate the remaining quantity of tritium. y = 25 * (1/2)^2 y = 25 * 1/4 y = 6.25

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