© JP 1 RADIOACTIVE DECAY

2 It is impossible to say when a particular nucleus will decay. It is only possible to predict what fraction of the radioactive nuclei will decay in a certain time. RADIOACTIVE DECAY OF ATOMS (TRANSMUTATION OF ATOMS) IS A RANDOM PROCESS RADIOACTIVE DECAY OF ATOMS (TRANSMUTATION OF ATOMS) IS A RANDOM PROCESS RANDOM

© JP 3 Radioactive Decay is not affected by: 1.Physical Conditions - like temperature or pressure. 2.Chemical Changes – it does not matter if the radioactive isotope is part of a compound. The half-life of a radioactive isotope is the average time it takes for half of its atoms to decay.

© JP 4 Number of atoms, N time, t Initial numb of atoms, N 0 HALF LIFE t 1/2 t 1/2 THE RATE OF DECAY DEPENDS UPON THE AMOUNT OF MATERIAL REMAINING, SO THE DECAY IS EXPONENTIAL

© JP 5 N0N0 N t λ = the decay constant – measures the probability of an atom decaying λ has units of seconds -1 When N = ½ N o, t = t 1/2

© JP 6 A0A0 A t As the Activity, A, depends upon the number of atoms in the source, the Activity also decays exponentially N.B. Active isotopes have short half lives

© JP 7 differentiating or i.e. The activity = the number of atoms in the source times the decay constant

© JP 8 UNITS OF ACTIVITY 1 Bq = one disintegration per second Gray (Gy) – the amount of radiation causing 1 kg of tissue to absorb 1 joule (J) of energy Other units Sievert (Sv) – Arbitrary unit, based on the Gray, but adjusted to account for damage to living tissue.

© JP 9 Example 1 A radioactive source contains 1 x g of plutonium – 239. The source is found to emit 2300 alpha particles per second in all directions. Find the half life of plutonium. 1.Finding the number of atoms present in 1 x g of plutonium – g contain 6.02 x atoms 3.Hence 1 x g contain 2.52 x atoms = N = λ x 2.52 x λ = 9.13 x s t 1/2 = 7.59 x s = years

© JP 10 Example 2 A compartment on a Geiger Müller tube is filled with a solution containing 1.00g of carbon extracted from one of the Dead Sea scrolls. This gives a count rate of 1000 per hour. When a similar solution containing 1.00 g of carbon extracted from a living plant is used instead, the count rate is 1200 per hour. With no solution in the compartment, the count rate is 300 per hour. Estimate the age of the scroll if the half life of carbon -14 is 5600 years. The original count rate corrected for background radiation is A 0 = 1200 – 300 = 900 counts per hour The corrected count rate after the sample has decayed for t years is A = 1000 – 300 = 700 counts per hour t = 2027 years

© JP 11 MEASUREMENT OF HALF LIFE 1. SIMPLY MEASURE AND PLOT HOW THE ACTIVITY VARIES WITH TIME MEASUREMENT OF SHORT HALF LIVES 2. READ OFF t 1/2 REPEAT AND AVERAGE !! OR PLOT A LOG GRAPH

© JP 12 MEASUREMENT OF HALF LIFE MEASUREMENT OF SHORT HALF LIVES LOG GRAPHS lnA t gradient = - λ

© JP 13 MEASUREMENT OF HALF LIFE MEASUREMENT OF LONG HALF LIVES 1. RECORD ACTIVITY 2. BY WEIGHING / CHEMICAL ANALYSIS FIND THE NUMBER OF MOLES OF MATERIAL PRESENT 3. USING AVOGADRO’S NUMBER, FIND THE NUMBER OF ATOMS PRESENT 4. APPLY TO FIND λ