Lecture 11. Half-Lives of Various Nuclides. Radioactive decays are all first order processes. Professor Hicks Inorganic Chemistry (CHE152)

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1 Lecture 11 Professor Hicks Inorganic Chemistry (CHE152) Radioactive decays are all first order processes Half-Lives of Various Nuclides Nuclide Half-Life Type of Decay Th x yr alpha U x 10 9 yr alpha C yr beta Rn sec alpha Th x 10 6 sec alpha 1

2 Carbon-14 dating study the slides on C-14 for their content cosmic radiation promotes Transmutation of nitrogen-14 to carbon N n 14 0 C p space donuts C 6 H 12 O 6 (sugar) photosynthesis 14 6 CO 2 Earth s atmosphere Earth Carbon-14 dating eating the donuts makes Homer slightly radioactive when Homer dies he stops replenishing the carbon-14 in his body and the amount that is there starts to decay space Earth s atmosphere Rest in Peace Earth 2

3 Carbon-14 dating almost all life is part of the same food chain plants make sugars animals eat plants animals eat animals %carbon-14 is constant for an organism constantly taking in food when they die they stop replenishing carbon-14 and the clock on its decay starts t ½ = 5730 years [ 14 C] = [ 14 C] initial e -kt useful for dating ,000 years Carbon-14 dating % C-14 (compared to living organism) Object s Age (in years) 100% 0 90% % % % % % 11,500 10% 19,000 5% 24,800 1% 38,100 8 Kinetics of radioactive decay first order process [Uranium-238] = [Uranium-238] initial e -kt [ ] s can be replaced with any quantity that proportional to the amount of element: mass, moles, volume under constant T, P, or rate of radiation emission Shorter half-life more decay per second - we say the sample is hotter and in many cases it is at higher temperature 3

5/15) = e -0.0001209*t 1 = e -k*5730 2 ln(1/2) = -k*5730 k = 1.209 x 10-4 yr -1 = 0.

4 Example: An ancient skull gives 4.50 particles/min gc. If a living organism gives 15.3 particles/min gc, how old is the skull? 1) use half-life t½ to find k 2) use the k value to solve for t use ratio of rates of particle emission instead of ratio of [ ] s [C-14] = e -kt [C-14] initial 1 2 = e -kt1/2 (4.5/15) = e *t 1 = e -k* ln(1/2) = -k*5730 k = x 10-4 yr -1 = yr -1 t = 9958 yr Albert Einstein Mass Defect and Binding Energy E = mc 2 Lise Meitner when a nucleus forms, some of the mass of the separate nucleons is converted into energy the difference in mass between the separate nucleons and the combined nucleus is called the mass defect the energy that is released when the nucleus forms is called the binding energy 4

5 binding energy = heat released when nucleus forms it comes from mass energy homer on the earth s surface E = mc 2 c = speed light m = mass defect amu here E = binding energy separated protons, neutrons total mass amu + + N N N N N N heat released heat released energy = binding energy mass homer trapped in the well b/c he Copyright does not 2009 have Charles energy Hicks to escape total mass = amu + + N N N N + N + + N N + carbon-12 nucleus compare elements binding energy per nucleon Iron-56 has the most stable nucleus energy will be released when: 14 Calculate the amount of energy released when a helium-4 nucleus is formed from two protons and two neutrons. This is also referred to as the binding energy of a helium-4 nucleus. Mass He-4 = Mass Neutron = Mass proton =

Fission/Fusion a few nuclei are so unstable that if their nucleus is hit by a neutron, the large nucleus splits into two smaller nuclei - this is called fission small

gram than fission Lise Meitner Fission where does the energy from fission/fusion come from?

6 Fission/Fusion a few nuclei are so unstable that if their nucleus is hit by a neutron, the large nucleus splits into two smaller nuclei - this is called fission small nuclei can be smashed together to make a larger nucleus - this is called fusion both fission and fusion release enormous amounts of energy fusion releases more energy per gram than fission Lise Meitner Fission where does the energy from fission/fusion come from? during nuclear fission, mass is converted into energy as a more stable nucleus forms the energy can be calculated from E=mc 2 U-235 that undergoes fission produces about 1.7 x J per mole a very exothermic chemical reaction produces around 10 6 J per mole 6

7 Fission Chain Reaction a chain reaction occurs when a reactant in the process is also a product of the process in fission it is neutrons small amount of neutrons start the chain many of the neutrons produced in fission are either ejected from the uranium before they hit another U-235 or are absorbed by the surrounding U-238 minimum amount of fissionable isotope needed to sustain the chain reaction is called the critical mass if sample is very dilute most neutrons will escape - they will not initiate another reaction if sample is absorbing more than 1 neutron on the average then the process will very rapidly accelerate - this is called a Criticality Excursion Criticality excursions Samples that are undergoing fission, releasing neutrons, can experience sudden accelerations due to nuclear chain reactions Caused by Precipitations Neutrons reflected back Change in shape of container All increase the number of emitted neutrons that are absorbed initiating the next step of the chain reaction Powerful bursts of radiation emitted 7

Nuclear Power Plants - Core fissionable material is stored in long tubes, called fuel rods, arranged in a matrix between the fuel rods are control rods made of neutron absorbing material B or Cd

8 Nuclear Power Plants - Core fissionable material is stored in long tubes, called fuel rods, arranged in a matrix between the fuel rods are control rods made of neutron absorbing material B or Cd neutrons needed to sustain the chain reaction when the rods are lowered slow down ejected neutrons, called a moderator allows rate of chain reaction to be controlled Nuclear Fusion Fusion potentially safer fuels than fission 4 + He n H 3 H 1 1 tritium relatively safe t ½ = 12 years beta decay problems 1) activation energy is high T ~ 10 8 K products not radioactive isotopes! 2) hard to create/control high enough temperatures 8

9 Fusion Cold Fusion???? (heat absorbed) heat released overall reaction Describe the effect of raising or lowering the control rods in a nuclear fission reactor 9

10 Estimate the energy released when 1.0 mole of Am-241 undergoes alpha decay. Mass Am-241 = amu Mass Np-237 = amu Mass He-4 = amu Compare the value you obtain to the amount of energy obtained from combustion of 1 mole of octane 5.0 x10 6 J/mol Example: If you have a 1.35 mg sample of Pu-236, calculate the mass that will remain after 5.00 years Pu-236 has a half life of 2.86 yr 1) use half-life t ½ to find k 2) use the k value and the t of interest to solve for mass at that time 10

cartilige contain substantial amounts of Ca and P which are larger nuclei absorb more radiation X-ray imaging Medical x-rays are of

11 Blocking radiation An elements ability to block X-rays increases with nuclear size (Z) Pb is often used as shielding because it is almost the heaviest element that is not radioactive itself Soft body tissue is mostly H 2 O, which is mostly O-16 by mass Bone and cartilige contain substantial amounts of Ca and P which are larger nuclei absorb more radiation X-ray imaging Medical x-rays are of the shadows of denser body tissue bones, cartilage, etc X-ray source CT Scans Series of x-rays used to construct a 3- dimensional image 11

PET Scan imaging technique based on positron emission positron + electron gamma rays isotope incorporated into a molecule molecule ingested

drugs that bind in the brain s addiction centers - F-18 labeled cocaine, heroine Barium Enema radiation absorption increases with size of

because Ba absorbs X-rays well Radiation therapy Cancerous tumors dosed with radiation Can be performed with focused beams, or seeding

12 PET Scan imaging technique based on positron emission positron + electron gamma rays isotope incorporated into a molecule molecule ingested positrons emitted from places molecule is concentrated gives a three dimensional x-ray of the region the molecule binds example F-18 labeled drugs that bind in the brain s addiction centers - F-18 labeled cocaine, heroine Barium Enema radiation absorption increases with size of nucleus bones Ca, P causes them to absorb more than soft tissue mostly H, O, C, N colon can be imaged with x-rays if it is filled with BaSO 4 because Ba absorbs X-rays well Radiation therapy Cancerous tumors dosed with radiation Can be performed with focused beams, or seeding radioactive material near the tumor, or Molecules labeled with radioactive isotopes that target specific organs Radiotherapy works by damaging the DNA of the cancer cells 12

Radiation therapy External beam radiation therapy Cobalt-60 often used as a source of radiation It is a

accumulates in the thyroid gland I-131 is radioactive and can be used to treat thyroid cancer I-131 after

Non-radioactive iodine is eaten to prevent damage to the thyroid caused by I-131 released from nuclear

not radioactive Radiation therapy Internal radiotherapy Prostate cancer treated with radioactive seeds

13 Radiation therapy External beam radiation therapy Cobalt-60 often used as a source of radiation It is a beta emitter beam is focused on the site of the tumor Radiation therapy Internal radiotherapy I naturally accumulates in the thyroid gland I-131 is radioactive and can be used to treat thyroid cancer I-131 after being ingested a NaI-131 accumulates in thyroid where it undergoes - decay dosing the thyroid cancer Non-radioactive iodine is eaten to prevent damage to the thyroid caused by I-131 released from nuclear bombs or accidents It works by flooding the body with I- so that most of the I - at the thyroid gland is not radioactive Radiation therapy Internal radiotherapy Prostate cancer treated with radioactive seeds Palladium-103 is an example of a seed material It has t ½ = 17 days decays by electron capture emitting gamma rays Pd-103 seeds 13

14 Dangers of Radioactivity high energy radioactive decay products called Ionizing Radiation Ionizing radiation can directly cleave DNA - called primary damage, or - can break molecules up forming species that cause damage by chemical reactions - called secondary damage most common secondary pathway is water OH absorbing radiation forming hydroxyl radicals radical = odd number of electrons Very reactive and an oxidizing agent Relative Biological Effectiveness (at causing damage) Type and Energy Range Relative Biological Effectiveness X and Gamma rays 1 Electrons 1 Neutrons (energy dependent) 10 Protons 5 Alpha Particles 20 you will be provided with this table on the exam Dose amount of energy absorbed in an exposure has a unit called the gray (Gr) 1 gray = 1 Joule kg tissue gray is a large unit for typical exposures A more common unit is the Radiation Absorbed Dose (RAD) 0.01 gray = 1 RAD 14

15 REM s unit used to measure total risk associated with a dose accounts for differences in extent of damage caused by different particle types dose in REM = dose in RAD x RBE typical x-ray deliver mrem background level is mrem per year barium enema recently? you got 400 mrem dose (REM) effect 5 none felt, yearly limit radiation workers 50 none felt, red blood cell count lowered 1000 near 100% fatal Factors besides size of dose Getting a dose in regions that are mostly muscle (legs, arms) is much less dangerous than the same dose in your organs Distributing a dose over time is much less damaging Cells have repair mechanisms If repair can keep up much less damage can accumulate - DNA single strand breaks are repairable - Double strand breaks not very repairable Dangers of radiation and penetrating power gamma radiation strongly penetrating requires thick layers of most protecting materials without protection dangerous doses quickly delivered and emitters easy to block and emitters very dangerous if ingested since they can deliver large doses accumulated over time 15

16 Why do beta emitters not have to be kept in a thick-walled lead containers, but precautions must be taken to prevent ingesting them? Calculate how many REMs were delivered in 10 barium enemas if the dose for each barium enema is 0.40 RAD How many RAD of alpha particles could a radiation worker be dosed with before they reached their yearly safety limit of 5.0 REM? 16

Lecture Presentation. Chapter 21. Nuclear Chemistry. James F. Kirby Quinnipiac University Hamden, CT Pearson Education, Inc.

Lecture Presentation. Chapter 21. Nuclear Chemistry. James F. Kirby Quinnipiac University Hamden, CT Pearson Education, Inc. Lecture Presentation Chapter 21, Inc. James F. Kirby Quinnipiac University Hamden, CT Energy: Chemical vs. Chemical energy is associated with making and breaking chemical bonds. energy is enormous in comparison.