Radioactive Decay and Half-Life

The average time taken for a radioactive parent atom to decay to half of its original mass is called the half-life. This does not mean that half of the original mass is lost, but rather decayed to its daughter atom.

Mass of radium-226

Half-life can be determined experimentally by chemically analyzing a sample for the amount of isotopes present or the amount of radiation emitted from the nucleus every second. This is called the activity, measured in Becquerels, Bq). One Becquerel represents the disintegration of one nucleus per second. A radiation detector, called a Geiger counter, measures activity as it drops off over time. As the activity of a sample decays, so does the mass and number of nuclei remaining in the radioisotope.

Where: A0 rep. the mass of the initial sample (or other relative quantity measurement…ex Bequerel. A rep. the mass remaining after decay. (or other relative quantity measurement) h rep. the half-life of the sample. t rep. the elapsed time of decay.

Sample Question Neon-19 has a half life of 17.22 s. What mass of neon-19 will remain from a 100.0 mg sample after 30.0 s? A0 = 100.0g; h= 17.22s, t= 30.0 s Therefore, approximately 30.0 g of neon-19 will remain after 30 s.

Sample Question The half-life of strontium-90 is 28 a. If a 60.0 g sample of strontium-90 is currently in a sample of soil, how much strontium-90 will be present in the soil 90 a later? A0 = 60.0 g; h = 28 a; t = 90 a; A = ? Therefore, approximately 6.46 g of strontium-90 will remain after 90 years.

Sample Question The isotope technetium-99 has a half-life of 6 hours. A new sample has just arrived on January 15th and has 720 Bq of activity. How long before it decays to one-third its activity? h = 6 hrs ; Ao = 720Bq; A = 0.333x (720Bq)= 240Bq ; t =? Therefore, approximately 9.51 hours will pass before one third of the sample decays.

Carbon-dating Carbon-14 has a half-life of 5730 years as it beta decays in the following manner: The amount of carbon-12 and carbon-14 are roughly equal in all organisms. When organisms die, all cellular processes cease, thereby halting the cycling of carbon. This starts the natural decay of carbon-14. Over time, the C-14 to C-12 ratio decreases. This allows the ability to approximate the age of organisms that once lived long ago!

Where: N0 rep. the number of radioactive nuclei at time 0. N rep. the number of radioactive nuclei after time t has elapsed. λ is equal to 0.693/h (h is the half life) t rep. the elapsed time of decay.

Sample Question A radioactive substance has a half-life of 383 d. If the original mass has 5.0 x 105 radioactive nuclei, how many nuclei are present after 14.6 d? ? N0 = 5.0 x 10 5; h= 3.83d, t= 14.6d; λ= 0.693/3.83= 0.181 d-1 Therefore, approximately 3.8 x 10 4 nuclei are left