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Q.

A fresh radioactive mixture contains short lived species A and B. Both emitting α-particles initially of 8000 α-particles per minute. 20 minutes later they emit at the rate of 3500 α-particles per minute. If the half-lives of the species A and B are 10 minutes and 500 hours respectively, then the ratio of activities of A : B in the initial mixture was:

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a

4 : 6

b

6 : 4

c

3 : 4

d

3 : 1

answer is D.

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Detailed Solution

Let initial activaties of A and B are A0 and B0∵ after 2 half-lives of activity of A will remain A04A0+B0=8000 and also A04+B0=3500(we can assume that activity of B remains constant due to larger half-life) 3A04=4500;A0=6000;B0=2000A0B0=60002000=31
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A fresh radioactive mixture contains short lived species A and B. Both emitting α-particles initially of 8000 α-particles per minute. 20 minutes later they emit at the rate of 3500 α-particles per minute. If the half-lives of the species A and B are 10 minutes and 500 hours respectively, then the ratio of activities of A : B in the initial mixture was: