At a particular time,a radioactive source A has a strength of 1.60 $\times$ 10¹¹ Bq and a half-life of 15.0 d,and a second source B has a strength of 8.50 $\times$10¹¹ Bq.Sources A and B have the same strength 45.0 d later.The half-life of B is A)0.19 d B)8.3 d C)2.8 d D)5.4 d E)28 d

Question

Quizplus · Accepted Answer

For source A, after 45.0 days, the fraction of the original strength remaining is:

(1/2)^(45/15) = 1/8

Therefore, the strength of source A after 45.0 days is:

1.60x10^10 Bq / 8 = 0.20x10^10 Bq

For source B, we can use the same equation:

(1/2)^(t/HL) = 1/8

Solving for t/HL, we get:

t/HL = 3

t = 3 HL

Substituting the given values, we get:

8.50x10^10 Bq / (1/2)^(45/t) = 0.20x10^10 Bq

Solving for t, we get:

t = 8.3 d

Therefore, the half-life of source B is 8.3 days.

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