______: the Time Required for One-Half of the Atoms of a Radioisotope to Emit Radiation

Lecture 17.3 Name______HALF-LIFE

______: The time required for one-half of the atoms of a radioisotope to emit radiation and to decay to the daughter nuclide. A. Parent nuclide: ______B. Daughter nuclide: ______C. Every radioisotope has a characteristic rate of decay measured in by its half-life. D. The half-life is the time it takes for ½ of the original radioactive atoms to decay into atoms of a new element. The other half remains unchanged.

II. The stability of a radioisotope is indicated by its half-life. A. The longer the half life, ______. B. Half lives vary from fractions of a second to millions of years. C. Most artificially produced isotopes have short half lives.

III. Carbon-14 Dating A. Carbon-14 is a radioactive nuclide constantly produced in the atmosphere. B. Carbon-14 has a half-life of 5730 years. C. Carbon-14 undergoes beta emission to form N-14: D. During photosynthesis, plants absorb CO2. A percentage of this CO2 is made from Carbon-14. E. When the plant dies, photosynthesis stops and no more radioactive CO2 is absorbed. The radioactive decay of carbon-14 continues. F. By knowing what % of carbon-14 a living plant contains and determining the % of carbon-14 the once-living plant now contains, scientists are able to determine the age (or the time in history that plant died). G. A sample of material is burned to convert carbon to CO2. The CO2 is trapped and frozen with liquid air, in order to measure the radioactivity with a counter. H. A newer technique would be to ionize the sample and pass it through a particle accelerator. The isotope is separated by the magnetic field and counted by a detector.

IV. Solving Half-Live Problems A. Five variables: 1) m0 = original mass or amount of the isotope present 2) mt = mass or amount of original isotope remaining at time t 3) t = the time elapsed 4) t½ = the half-life 5) n = number of half-lives elapsed during time t V. Examples:

A. What mass of an isotope remains after 10.5 years if you start with 25.0 g? The half-life of this isotope is 3.5 years.

B. How long would it take for a sample to decay to 12.5% of its original mass if the half-life is 500.0 years?

C. If only 1/32 of an original sample remains after 30 years, what is the half-life of this isotope?

D. What mass of a radioactive sample was originally present if 4.70 g. remain after 20.0 minutes. The half-life of this isotope is 5.00 minutes. Hw 17.3 Name______HALF-LIFE HOMEWORK

1) A sample of polonium-218 weighing 50.0 g. is stored on a laboratory shelf. How much of the isotope will remain after 15 minutes have passed? The half-life of polonium-218 is 3.0 minutes.

2) How long will it take a piece of strontium-90 (produced in a nuclear test blast) weighing exactly 1.000 kg to be reduced to 15.6g.? The half-life of strontium-90 is 28.8 years.

3) A meteorite strikes the earth in western Wyoming. Chemical analysis shows it contains 44.62kg. of radioactive iron-59. How much of this isotope will remain in the meteorite after 310 days? The half-life of iron-59 is 44.3 days.

4) How much time will be required for a sample of plutonium-239 to lose 50.0% of its radioactivity? The half- life of plutonium-239 is 24.36 years.

5) How long will it be before only 1/16 of an original sample of radon-222 remains? The half-life of radon-222 is 3.8 days. 6) A piece of wood is known to be 34320 years old. At the present time, the wood contains 4.00g. of carbon- 14. How much carbon-14 was in the wood originally? The half-life of carbon-14 is 5720 years.

7) A block of platinum-197 weighs 250 g. How much of the platinum-197 will remain in 3.75 days? The half- life of platinum-197 is 18 hours.

8) The decay of a sample of tritium gas has been carefully monitored for just slightly less than 37 years. The weight of the tritium in the sample today is 6.40 g. What was the weight of the tritium in the sample originally? The half-life of tritium is 12.5 years.

9) A radioactive isotope decays to one-eighth of its original activity in 60 years. What is the half-life of this isotope?

10) In studies to determine the half-life of an isotope, 10.0 g. of the isotope is found to decay to 0.625 g. over a period of 6.0 hours. From this information, calculate the half-life of the isotope.