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A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 srespectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in themixture will become equal after : [2012]
- a)60 s
- b)80 s
- c)20 s
- d)40 s
Correct answer is option 'D'. Can you explain this answer?
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A mixture consists of two radioactive materials A1 and A2 with half li...
Explanation:
Given:
- Half-life of A1 = 20 s
- Half-life of A2 = 10 s
- Initial amount of A1 = 40 g
- Initial amount of A2 = 160 g
Approach:
- Calculate the decay constant (λ) for each radioactive material using the formula: λ = ln(2) / half-life
- Use the decay equation N(t) = N0 * e^(-λt) to find the amount of A1 and A2 after a certain time t
- Set the amounts of A1 and A2 equal to each other to find the time at which they become equal
Calculations:
- Decay constant for A1 (λ1) = ln(2) / 20 = 0.03465 s^-1
- Decay constant for A2 (λ2) = ln(2) / 10 = 0.0693 s^-1
- Amount of A1 at time t: N1(t) = 40 * e^(-0.03465t)
- Amount of A2 at time t: N2(t) = 160 * e^(-0.0693t)
- Set N1(t) = N2(t) to find the time at which the amounts become equal:
40 * e^(-0.03465t) = 160 * e^(-0.0693t)
e^(-0.03465t) = 4 * e^(-0.0693t)
-0.03465t = ln(4) - 0.0693t
0.03465t = 0.6931
t ≈ 20 s
Conclusion:
The amount of A1 and A2 in the mixture will become equal after approximately 20 seconds. Therefore, the correct answer is option 'D'.
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A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 srespectively. Initially the mixture has 40 g of A1and 160 g of A2. The amount of the two in themixture will become equal after : [2012]a)60 sb)80 sc)20 sd)40 sCorrect answer is option 'D'. Can you explain this answer?
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A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 srespectively. Initially the mixture has 40 g of A1and 160 g of A2. The amount of the two in themixture will become equal after : [2012]a)60 sb)80 sc)20 sd)40 sCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 srespectively. Initially the mixture has 40 g of A1and 160 g of A2. The amount of the two in themixture will become equal after : [2012]a)60 sb)80 sc)20 sd)40 sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 srespectively. Initially the mixture has 40 g of A1and 160 g of A2. The amount of the two in themixture will become equal after : [2012]a)60 sb)80 sc)20 sd)40 sCorrect answer is option 'D'. Can you explain this answer?.
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