Radioactive Decay The nuclei of some chemical elements are unstable against the strong nuclear force holding them together, resulting in a spontaneous change of characteristic or identity of the element. This is especially common for elements above 92 There are 3 methods of decay

Decay Mechanisims  - decay  - decay  - decay A Helium nucleus seems to emerge from the unstable element An electron and neutrino emerge from the unstable element A photon emerges from the unstable element

 - decay Helium nucleus emerges from the unstable element U  Th He + energy electric repulsion becomes greater than the nuclear attraction/ contrast between short and long range forces. Masses do not balance! …Why?

 - decay An electron and a “neutrino” emerge from the unstable nucleus C  7 14 N e + energy Weak force - a “down quark” in a neutron changes into an “up quark” changing it into a proton. Masses do not balance! …Why?

 - decay Photon emerges from the unstable element The element retains its identity Al*  Al +  + energy nucleus is not changed but has an excess of energy - particles are agitated and farther away from each other. Masses don’t balance!

Einstein - mass IS energy E =  mc 2  m is the mass difference between the parent nuclei and the daughters. The equation gives the energy released. Mass is converted into energy!

Decay Process The fraction of atoms decaying in a time interval  t is: –The value of depends on the nucleus –The unit of is 1/seconds (per second)  N / N = -  t

Decay Measurement In the Lab Measuring λ for an element: Villanovium  N / N = -  t 1. How may atoms of Villanovium? 3. Count decay particles during time interval 2. Timer for Geiger Counter Vu

The Decay Equation The fraction of atoms decaying in a time interval  t is: Using calculus on this equation, we get: N(t) - # at time t N 0 - # at beginning t - elapsed time e = …  N / N = -  t N(t) / N 0 = e - t

Decay Equation – how it works How does N(t) decrease with time? N(t) / N 0 = e - t

ADD a fraction each time – compound interest N(t) / N 0 = e + t

Decay Equation – how it works Suppose 10% decays each second: N(t) / N 0 = e - t 50%, half-life 

Half-Life – when ½ remains Half-life [ t ½ ] when 10% decays in a second --- about 6.4 seconds N(t) / N 0 = e - t NEVER REACHES 0 Seconds

If you know, you can find t 1/2 Suppose that 50% is left, then: Since we know we can solve for “t 1/2 ”. We call that time the half-life – how long it takes (in seconds) for ½ of the sample to decay. N(t) / N 0 = e - t = 0.5

Half-life examples Isotope Half- Life Cesium Years Chromium Days Cobalt Days Cobalt Years Copper Hours Fluorine Min Gadolinium Days Gallium Days Gold Days Indium Days Iodine Hours Iodine Days Iodine Days Isotope Half- Life Iridium Days Molybdenum Hours Phosphorus Days Samarium Hours Selenium Days Strontium Days Technetium 99m 6.01 Hours Thallium Days Xenon Days Yttrium Hours