Half-lives of two radioactive nuclei A and B | vedclass

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(A) Let the initial number of nuclei be $N_0$ for both $A$ and $B$. For nucleus $A$,half-life $T_{1/2, A} = 10 \, min$. After $t = 60 \, min$,the numb

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$9 : 8$

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(A) Let the initial number of nuclei be $N_0$ for both $A$ and $B$. For nucleus $A$,half-life $T_{1/2, A} = 10 \, min$. After $t = 60 \, min$,the number of half-lives $n_A = 60/10 = 6$. The number of undecayed nuclei $N_A = N_0 / 2^6 = N_0 / 64$. The number of decayed nuclei $D_A = N_0 - N_A = N_0(1 - 1/64) = 63N_0 / 64$. For nucleus $B$,half-life $T_{1/2, B} = 20 \, min$. After $t = 60 \, min$,the number of half-lives $n_B = 60/20 = 3$. The number of undecayed nuclei $N_B = N_0 / 2^3 = N_0 / 8$. The number of decayed nuclei $D_B = N_0 - N_B = N_0(1 - 1/8) = 7N_0 / 8$. The ratio of decayed nuclei $D_A / D_B = (63N_0 / 64) / (7N_0 / 8) = (63/64) 	imes (8/7) = 9/8$.

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be:

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