Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially the samples have equal number of nuclei. After 80 minutes the ratio of decayed numbers of A and B nuclei will be:

1 : 16

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4 : 1

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1 : 4

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5 : 4

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Solution

The correct option is D $5 : 4$
After 80min. for first element, number of nuclei left will be $N_{1} = N (1 - \frac{1}{16}) = \frac{15 N}{16}$ .

Similarly, for second element, $N_{2} = N (1 - \frac{1}{4}) = \frac{3 N}{4}$

The ratio $\frac{N_{1}}{N_{2}} = \frac{5}{4}$

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Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially the samples have equal number of nuclei. After 80 minutes the ratio of decayed numbers of A and B nuclei will be:

The correct option is D 5:4After 80min. for first element, number of nuclei left will be N1=N(1−116)=15N16.Similarly, for second element, N2=N(1−14)=3N4The ratio N1N2=54

The correct option is D $5 : 4$
After 80min. for first element, number of nuclei left will be $N_{1} = N (1 - \frac{1}{16}) = \frac{15 N}{16}$ .

Similarly, for second element, $N_{2} = N (1 - \frac{1}{4}) = \frac{3 N}{4}$

The ratio $\frac{N_{1}}{N_{2}} = \frac{5}{4}$