Some nuclei are unstable and decay at a rate of 432 per...

Some nuclei are unstable and decay at a rate of 432 per second at t = 15 minutes. At t = 48 minutes, the counting rate has fallen to 213 per second. a/ What is the half-life of the radioactivity? b/ What will be the decay rate at t = 100 minutes?

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Transcript

00:01 Hello everyone.

00:02 In the present problem it is given that rate of decay is 432 per second at t is equal to 15 minutes.

00:13 At t is equal to 48 minutes, counting rate is 230 per second.

00:20 Coming to the solution, we have.

00:29 Suppose initial unstable nuclei is equal to n.

00:44 At t is equal to 15 minutes we have d n divided by d t is equal to plus lambda n here n1 is the number of undecade nucleide at t is equal to 15 minutes.

01:36 Therefore, 432 is equal to plus lambda n1.

01:43 Let this be equation 1.

01:48 At t2 is equal to 48 minutes we have d n divided by d t is equal to is equal to.

02:03 Plus lambda n2.

02:08 N2 is number of undecade nuclei at t is equal to 48 minutes.

02:30 This implies 213 is equal to plus lambda n2.

02:41 Let this be equation 2.

02:53 Dividing equation 1 by equation 2 we have 432 divided by 213 is equal to plus lambda n1 divided by plus lambda n2 is equal to n1 divided by n2.

03:18 Let this be equation 3.

03:21 We know n0 e raised to minus lambda t.

03:36 So 432 divided by 213 is equal to n0 e raised to minus lambda t1 divided by n0 e raised to minus lambda t1 divided by n0 e raised to minus lambda t2.

03:56 This is equal to e raised 2 minus lambda t1 minus of minus lambda t2...

Question

Some nuclei are unstable and decay at a rate of 432 per second at t = 15 minutes. At t = 48 minutes, the counting rate has fallen to 213 per second. a/ What is the half-life of the radioactivity? b/ What will be the decay rate at t = 100 minutes?

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