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4. A radioactive isotope has a half-life of 76.0 min. A sample is prepared that has an initial activity of 16.0E10 Bq.

a. How many radioactive nuclei are initially present in the sample? Answer:1.05E nuclei

b. How many are present after 76.0 min? Answer: 5.25E14 nuclei

d. How many radioactive nuclei are present 152.0 min after the sample was first prepared? Answer: 2.62E14 nuclei

e. What is the activity after 152.0 min? Express answer in Bq.Answer: 4.0E10 Bq

Added Sun, 23 Aug '15

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Law of radioactive decay:

N = No e^{-kt}

Half-life, t_{1/2} = 0.693 / k

Thus, 0.693 / k = 76 * 60 or k = 1.5197E-4

Law of radioactive decay:

dN/dt = -kN = -k(m/M)N

or 16.0E10 Bq = - 1.5197E-4 * N

or N = **10.5E14** ignoring negative sign

After 76 min,

N = 10.5E14 * e^{-1.5197E-4*76*60}

= 10.5E14 * e^{-0.69298}

= 10.5E14 * 0.5

= **5.25E14**

After 152 min,

N = 10.5E14 * e^{-1.5197E-4*152*60}

= 10.5E14 * e^{-1.386}

= 10.5E14 * 0.25

= **2.625E14**

Activity after 152 min = kN = 2.625E14 * 1.5197E-4

= **3.989E10**

Added Sun, 23 Aug '15

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