Nuclei A and B convert into a stable nucleus C. Nucleus A is converted into C by emitting \( 2 \....

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Counter-Strike: Source
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Counter-Strike: Source (2004)
Duration: 2:56
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Nuclei A and B convert into a stable nucleus C.
\( \mathrm{P} \)
Nucleus A is converted into C by emitting \( 2 \alpha \) particles and \( 3 \beta \)-particles. Nucleus B is converted into \( \mathrm{C} \) by emitting one \( \alpha \)-particle and \( 5 \beta \)-particles. At time \( \mathrm{t}=0 \), nuclei of \( \mathrm{A} \) are \( 4 N_{0} \) and nuclei of B are \( N_{0} \). Initially number of nuclei of \( C \) are zero. Half-life of \( \mathrm{A} \) (into conversion of \( \mathrm{C} \) ) is 1 minute and that of \( \mathrm{B} \) is 2 minutes.
Find the time at which rate of disintegration of \( \mathrm{A} \) and \( B \) are equal (in minute).


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