12 IsotopeAtomic nuclei having the same number of protons but different number of neutrons
13 All Elements Have Radioactive Isotopes All elements have more than one isotopeSome isotopes of all elements are radioactiveSome half-lives are so short that the isotope is not found naturallyRadioactive Isotope display
14 A Half-Life Is the Time Required for ½ the Atoms of a Substance to Undergo Radioactive Decay Applet AnimationT1/2 = time for half the sample to disintegrateAssume T1/2 = 5 yearsNumber of nuclei present at time t = 0:N0 =When t = 5 yrs, N = 50t = 10 yrs, N = t = 20 yrs, N = 125.Calculate the half-life animation
32 Carbon DatingSince living organisms continually exchange carbon with the atmosphere in the form of carbon dioxide, the ratio of C-14 to C-12 approaches that of the atmosphere.From the known half-life of carbon-14 and the number of carbon atoms in a gram of carbon, you can calculate the number of radioactive decays to be about 15 decays per minute per gram of carbon in a living organism.
33 Measuring the Age of Organic Matter A German tourist in the Italian Alps discovered the remains of the "Iceman" in the ice of a glacier in
34 Calculating the Iceman's Age The current activity per gram of carbon half what it would be if the Iceman were alive. Since the half-life of carbon-14 is about 5700 years, the Iceman's remains are about 5700 years old.
35 Radioactivity Equations N(t) = population at time t N(0) = population at time zero N0 = N(0) l = decay constantExample: N0 = 1000l = 2 x 10-3 years -1 When will N = 200?N = N0 e-lt (1)e-lt = N /N0 (2)ln (e-lt) = ln (N /N0) (3)-l t = ln (N /N0) (4) N(t) = N0 e-lt t = - [ln (N /N0)] / l (5)= - [ln (200/1000)] /2 x10-3 (6)= 805 years
36 Half-Life ProblemThe half-life of a radioactive substance is 10 hours. What is the decay constant, l? N = N0 e-lt (1)0.50 N0 = N0 e-l10 (2)e-l10 = 0.50 (3)ln(e-l10) = ln(0.50) (4)-10 l = (5)l = hrs-1 (6)
37 Half-Life ProblemFrom the previous problem, how much time will it take for the sample's activity to fall to only 20% of what it was originally? N = 0.20 N0 (7)0.20 N0 = N0 e t (8)t = ln (0.20) (9)t = 23 hours
39 Half-Life Example38Sr90 (strontium-90) has a half-life of 28.5 years. How long will it take for 98% of a sample of strontium-90 to disappear? l = 0.693/T1/2= / 28.5= years-1 0.02 = e tt = - ln(0.02) / years-1= 161 years
40 Radioactivity UnitsA = number of disintegrations per second, activity A = lN One becquerel (Bq) is one disintegration per second. One curie is the number of disintegrations per second (the "activity") of one gram of radium, or about 3.7 x Bq.
41 Units of Absorbed Radiation Rad: 10 milli-joules per kilogram 20 rads of X-rays doesn't do the same damage to humans as 20 rads of alpha particlesRem: an absolute biological damage unit
43 Calculate Rems from Rads (Relative Biological Effectiveness) RadiationR(rems/rad)a-particles 20Neutrons 10Protonsb-particles 1g-rays 1X-raysExample: One joule of energy per kilogram is absorbed in the form of neutrons. Will this prove fatal?1 rad is ten milli-joules 1 rad = JExample: How many rads of protons will kill a person?600 rems is fatalRBE for protons is 10 Number of rads = 600 / 10 = 60
44 Radon PoisoningUranium in earth's crust decays to radium, which decays to radon.Radon is an odorless, tasteless, lighter-than-air gas which rises from the ground through cracks and fissures in the earth into homes. When breathed, the alpha- emitting radon can cause cancer of the lung.Radon is the single greatest source of radiations for humans, providing about 200 milli-rems per year per person.
45 Practice: Complete any four problems from the Radioactivity Worksheet When you are finished, raise your hand so I can stamp itBring this paper to school with you this week!