18.1: The half-life of ₇¹⁶N is 7.3 s. A sample of this nuclide of nitrogen is observed for 29.2s. Calculate the fraction of the original radioactive isotope remaining after this time.  Ans. (1/16)


18.2: Cobalt-60 is a radioactive element with half-life of 5.25 years. What fraction of the original sample will be left after 26 years? Ans. (1/32)

18.3: Carbon-14 has a half-life of 5730 years. How long will it take for the quantity of carbon-14 in a sample to drop to one-eighth of the initial quantity? Ans. (1.72 × 104 years).


18.4: Technetium-99m is a radioactive element and is used to diagnose brain, thyroid, liver and kidney diseases. This element has half-life of 6 hours. If there is 200 mg of this technetium present, how much will be left in 36 hours. Ans.(3.12 mg)


18.5: Half-life of a radioactive element is 10 minutes. If the initial count rate is 368 counts per minute, find the time by which, count rate would reach 23 counts per minute. Ans. (40 minutes)


18.6: In an experiment to measure the half-life of a radioactive element, the following results were obtained: 

Count rate (per minutes

400

  200

 100

 50

 25 

 Time (in minutes)

0

 2

 4

 6

 8

Plot a graph between the count rate and time in minutes. Measure the value for the half-life of the element from the graph. Ans. (half-life is 2 minutes)


18.7: A sample of certain radioactive element has a half-life of 1500 years. If it has an activity of 32000 counts per hour at the present time then plot a graph of the activity of this sample over the period in which it will reduce to 1/16 of its present value.


18.8: Half-life of a radioactive element was found to be 4000 years. The count rates per minute for 8 successive hours were found to be 270, 280, 300, 310, 285, 290, 305, 312. What does the variation in count rates show? Plot a graph between the count rates and time in hours. Why is the graph a straight line rather than an exponential? Ans. (Variation in count rate shows the random nature of radioactive decay, graph is almost horizonta


18.9: Ashes from a campfire deep in a cave show carbon-14 activity of only one-eighth the activity of fresh wood. How long ago was that campfire made? Ans. (17190 years)