introduction-to-radioactivity
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 introduction-to-radioactivity introduction-to-radioactivity Presentation Transcript

  • Atomic number = # of protons in nucleus THE PERIODIC TABLE# of nucleons = # of protons + # of neutrons OF ELEMENTSThe number of neutrons can vary slightly for a given element (isotopes)Atomic weight is equal to average number of nucleons in nucleus
  • Radioactivity: Birth of a new scienceMilestones (important events) leading to establishment of nuclearscience as a subjectDiscovery of X-Rays by W.C. Roentgen X-Discovery of Radioactivity by H. BecquerelDiscovery of Polonium and Radium by Marie and Pierre CuriesDiscovery of electron by J.J. ThompsonClassification of radioactive emissions by E. RutherfordDiscovery of atomic nucleus by E. RutherfordEnunciation of Rutherford-Soddy displacement law Rutherford-Discovery of neutron by J. ChadwickDiscovery of artificial radioactivity by Irene and J. CuriesDiscovery of nuclear fission by O. Hahn and Strassmann
  • Atomic Structure Inner electron shellProton NucleusNeutron Outer electron shell
  • Relative scale model of an atom and the solar system Do you perceive a gold ring to contain a larger fraction of solid matter than the solar system?On this scale, the nearest star would be a little over 10,000 milesaway
  • Nuclear notation• Z = atomic number or proton number, is the number of protons in the nucleus.• N = neutron number, is the number of neutrons in the nucleus.• A = Z + N = mass number, is the number of nucleons in the nucleus. A• In general, the notation is Z X N• For example, 12 C6 has atomic mass 12.000 6
  • Radioactivity• Questions – How and why do nuclei decay? – How do we use nuclear decay to tell time? – What is the evidence for presence of now extinct radionuclides in the early solar system? – How much do you really need to know about secular equilibrium and the U-series?• Tools – First-order ordinary differential equations
  • Enrico Fermi (1901-1954)-------------------------------One fermi (f) = 10-15 m
  • r = 1.2 A1/3 (in f)------------------------- Helium: A = 4 r = 1.2 (4)1/3 = 1.9 f------------------------- Uranium: A = 238 r = 1.2 (238)1/3 = 7.4 f
  • Protons which would Beyond about one fermi otherwise strongly repel the strong force declines at close distances are extremely rapidly. held in place by an extremely strong, but As more protons are extremely short range added to the nucleus, force called the strong more neutrons are force. Other names for needed to bind the the strong force are protons together, but strong nuclear force, or the larger the nucleus nuclear force. becomes, the farther apart are the protons STRONG FORCE The strong force between and the less effective two protons is about the is the strong forceProtons and neutrons in same as the strong forcethe nucleus are between two neutrons, orcollectively referred to as a proton and a neutron. nucleons.
  • Isotopes: Nuclides with same atomic number but different atomicweight (or different neutron number)All the nuclides belong to the same element 1 2 3 12 13 39 40 411H , 1H (D), 1H (T) 6C , 6C 19K , 19K , 19K 234, U235, U23892U 92 92Isobars: Nuclides with same atomic weight but different atomicnumber (Nuclides belong to different elements)18 Ar40, 19K40, 20Ca40Isotones: Nuclides with the same number of neutrons. 12 135B , 6C both have 7 NeutronsMirror nuclei: Nuclides with neutron and proton numberinterchanged7 N15 and 8O15
  • In general, the mass defect is calculated by summing the mass ofprotons, neutrons, and electrons in an atom, and subtracting theatom’s actual atomic mass. The general formula is:Md = Zmp + Nmn - MaWhere Z is the atomic number, N is the number of neutrons in theatom, and Ma is the actual measured mass of the atom. Placing Mdinto Einsteins equation for relating mass and energy gives theenergy release from forming the atom from its constituentparticles:E = Mdc2
  • Electric force is longer rangethan the strong force.Eventually separation becomestoo great for the strong force tocompensate for the repulsiveforces.Nuclei spontaneouslydisintegrate for proton numberslarger than 83.The release of light and orparticles which accompaniesthe disintegration is calledradiation, first discovered byHenri Becquerel in 1896.
  • Fundamental law of radioactive decay• Each nucleus has a fixed probability of decaying per unit time. Nothing affects this probability (e.g., temperature, pressure, bonding environment, etc.) [exception: very high pressure promotes electron capture slightly]• This is equivalent to saying that averaged over a large enough number of atoms the number of decays per unit time is proportional to the number of atoms present. dN• Therefore in a closed system: = − λN (Equation 3.1) dt – N = number of parent nuclei at time t – λ = decay constant = probability of decay per unit time (units: s–1)• To get time history of number of parent nuclei, integrate 3.1: N (t ) = No e− λt (3.2) – No = initial number of parent nuclei at time t = 0.
  • Definitions • The mean life τ of a parent nuclide is given by the number present divided by the removal rate (recall this later when we talk about residence time): N 1 τ= = λN λ – This is also the “e-folding” time of the decay: − λτ −1 No N (τ ) = No e = Noe = e • The half life t1/2 of a nucleus is the time after which half the parent remains: No − λt1/2 ln 2 .693N (t1/ 2 ) = = Noe ⇒ λt1/ 2 = ln2 ⇒ t1/2 = ≈ (3.3) 2 λ λ • The activity is decays per unit time, denoted by parentheses: ( N ) = λN (3.4)
  • Decay of parent λNo 0 ln(λN)–ln(λNo) -1 Activity λNo -2 slope = -1 2 λNo -3 e -4 -5 0 t 1/2 τ 2τ 3τ 4τ 5τ 0 t 1/2 τ 2τ 3τ 4τ 5τ time timeSome dating schemes only consider measurement of parent nucleibecause initial abundance is somehow known. • 14C-14N: cosmic rays create a roughly constant atmospheric 14C inventory, so that living matter has a roughly constant 14C/C ratio while it exchanges CO2 with the environment through photosynthesis or diet. After death this 14C decays with half life 5730 years. Hence even through the daughter 14N is not retained or measured, age is calculated using: 14 1 ( C) / C t= ln 14 [ λ14 ( C) / C ]o
  • Modes of decay• A nucleus will be radioactive if by decaying it can lower the overall mass, leading to larger (negative) nuclear binding energy – Yet another manifestation of the 2nd Law of thermodynamics• Nuclei can spontaneously transform to lower mass nuclei by one of five processes – α-decay – β-decay – positron emission – electron capture – spontaneous fission• Each process transforms a radioactive parent nucleus into one or more daughter nuclei.
  • α-decay Emission of an α-particle or 4He nucleus (2 neutrons, 2 protons) α-decay The parent decreases its mass number 238 by 4, atomic number by 2. 92 U # pr ot ons 91 Example: 238U -> 234Th + 4He 234 90 Th Mass-energy budget: 23 23 238U 238.0508 amu 8 144 145 146 23 23 # neutrons s 7 7 7 7 2 2 2 2 on 234Th –234.0436 3 3 3 36 le 2 uc 4He 35 35 n –4.00260 2 23 # 4 4 mass defect 0.0046 amu AX → A−4Y + 4He = 0.0046 x 930.5 = 4.5 MeV Z Z −2 2 X is called the parent nucleus and Y is called the daughter nucleusThis is the preferred decay mode of nuclei heavier than 209Bi with a proton/neutron ratio along the valley of stability
  • β-decay Emission of an electron (and an antineutrino) during conversion of a neutron into a proton The mass number does not change, β-decay the atomic number increases by 1. # prot ons 87 38 Sr Example: 87Rb -> 87Sr + e– + ν 37 87 Rb Mass-energy budget: 49 50 87Rb 86.909186 amu 8 88 # neutrons n s eo 87 87 l 87Sr –86.908882 uc 86 86 86 86 n # mass defect 0.0003 amu = 0.0003 x 931 = 0.28 MeVThe emission of the electron is from the nucleus The nucleus contains protons and neutrons The process occurs when a neutron is transformed into a proton and an electron Energy must be conserved This is the preferred decay mode of nuclei with excess neutrons compared to the valley of stability
  • Beta Decay• Symbolically A A − Z X→ Y + e + ν Z +1 A A Z X→ Z−1Y + e + + ν – ν is the symbol for the neutrino – ν is the symbol for the antineutrino• To summarize, in beta decay, the following pairs of particles are emitted – An electron and an antineutrino – A positron and a neutrino
  • β+-decay and electron captureEmission of a positron (and a neutrino) or capture of an inner-shell electron during conversion of a proton into a neutron Electron Capture The mass number does not change, # prot ons 19 K 40 the atomic number decreases by 1. 40 18 Ar 21 22 4 41 s Examples: 40K -> 40Ar + e+ + ν # neutrons n 4 4 eo 50V+ e– -> 50Ti + ν + γ 0 0 cl 39 39 39 39 nu # In positron emission, most energy is liberated by remote matter-antimatter annihilation. In electron capture, a gamma ray carries off the excess energy. These are the preferred decay modes of nuclei with excess protons compared to the valley of stability
  • Gamma Decay• Gamma rays are given off when an excited nucleus “falls” to a lower energy state – Similar to the process of electron “jumps” to lower energy states and giving off photons• The excited nuclear states result from “jumps” made by a proton or neutron• The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emission• Example of a decay sequence 12 B→12 C * + e − + ν 5 6 – The first decay is a beta emission 12 6 C*→12 C + γ 6 – The second step is a gamma emission
  • Spontaneous Fission Certain very heavy nuclei, particular those with even mass numbers (e.g., 238U and 244Pu) can spontaneously fission. Odd-mass heavy nuclei typically only fission in response to neutron capture (e.g., 235U, 239Pu) 10 There is no fixed daughter product but rather a 235 statistical distribution of fission products with U+n two peaks (most fissions are asymmetric). 1 Because of the curvature of the valley ofFission Yield ( %) stability, most fission daughters have excess 0.1 neutrons and tend to be radioactive (β-decays). 0.01 You can see why some of the isotopes people worry about in nuclear fallout are 91Sr and 137Cs. 0.001 Recoil of daughter products leave fission tracks of damage in crystals about 10 µm long, which only heal above ~300°C and are therefore useful0.0001 for low-temperature thermochronometry. 80 100 120 140 160 180 Atomic Mass (amu)
  • Natural Radioactivity• Classification of nuclei – Unstable nuclei found in nature • Give rise to natural radioactivity – Nuclei produced in the laboratory through nuclear reactions • Exhibit artificial radioactivity• Three series of natural radioactivity exist – Uranium-235 (4n + 3 series) Uranium- ends at Pb-207 Pb- – Uranium-238 (4n + 2 series) Uranium- ends at Pb-206 Pb- – Thorium-232 (4n series) Thorium- ends at Pb-208 Pb- 4n + 1 series starting from Neptunium-237 is extinct Neptunium- ends at Bi-209 Bi-
  • Uses of Radioactivity• Carbon Dating – Beta decay of 14C is used to date organic samples – The ratio of 14C to 12C is used• Smoke detectors – Ionization type smoke detectors use a radioactive source to ionize the air in a chamber – A voltage and current are maintained – When smoke enters the chamber, the current is decreased and the alarm sounds• Radon pollution – Radon is an inert, gaseous element associated with the decay of radium – It is present in uranium mines and in certain types of rocks, bricks, etc that may be used in home building – May also come from the ground itself
  • Nuclear Reactions• Structure of nuclei can be changed by bombarding them with energetic particles – The changes are called nuclear reactions• As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation
  • Which of the following are possible reactions? (a) and (b). Reactions (a) and (b) bothconserve total charge and total mass number as required. Reaction (c) violates conservation of mass number with the sum of the mass numbers being 240 before reaction and being only 223 after reaction.
  • Determine the product of the reaction 7 Li + 4 He → X ? + n 3 2 YWhat is the Q value of the reaction? In order to balance the reaction, the total amount ofGiven: nucleons (sum of A-numbers) must be the same on both sides. Same for the Z-number.reaction Number of nucleons (A): 7 + 4 = X + 1 ⇒ X = 10 Number of protons (Z): 3+ 2 = Y + 0 ⇒ Y = 5 Thus, it is B, i.e. 7Find: 3 Li + 2 He → 10 B + 01n 4 5Q=? The Q-value is then ( ) Q = ( ∆m ) c 2 = m7 Li + m 4 He − m10 B − mn c 2 = −2.79MeV
  • Processes of Nuclear Energy• Fission – A nucleus of large mass number splits into two smaller nuclei• Fusion – Two light nuclei fuse to form a heavier nucleus• Large amounts of energy are released in either case
  • Nuclear Fission• A heavy nucleus splits into two smaller nuclei• The total mass of the products is less than the original mass of the heavy nucleus• First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi• Lisa Meitner and Otto Frisch soon explained what had happened• Fission of 235U by a slow (low energy) neutron 1 0 n+ 235 U→236 U* → X + Y + neutrons 92 92 – 236U* is an intermediate, short-lived state – X and Y are called fission fragments • Many combinations of X and Y satisfy the requirements of conservation of energy and charge
  • Sequence of Events in Fission • The 235U nucleus captures a thermal (slow-moving) neutron • This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to undergo violent oscillations • The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion • The nucleus splits into two fragments, emitting several neutrons in the process
  • Natural (radioactive) decay (fission)Neutron-induced fission • Many heavy elements (eg. Uranium) decay (slowly) into lighter elements (natural decay) • However, this fission can also be induced by an incoming neutron. • Fission reaction release a lot of energy. • Fission often creates new neutrons!!
  • Fission andchain reactionFission releases neutrons …… these neutrons cause new fissionreactions in surrounding Uranium …… creating more neutrons …… chain reaction
  • Energy in a Fission Process• Binding energy for heavy nuclei is about 7.2 MeV per nucleon• Binding energy for intermediate nuclei is about 8.1 MeV per nucleon• Therefore, the fission fragments have less mass than the nucleons in the original nuclei• This decrease in mass per nucleon appears as released energy in the fission event• An estimate of the energy released – Assume a total of 236 nucleons – Releases about 0.9 MeV per nucleon • 8.1 MeV – 7.2 MeV – Total energy released is about 212 Mev• This is very large compared to the amount of energy released in chemical processes
  • Chain Reaction • Neutrons are emitted when 235U undergoes fission • These neutrons are then available to trigger fission in other nuclei • This process is called a chain reaction–If uncontrolled, aviolent explosion canoccur–The principle behindthe nuclear bomb, where1 g of U can releaseenergy equal to about20000 tons of TNT
  • Carbon dating is a variety of radioactive dating which is applicable only to matter which was once living and presumed to be in equilibrium with the atmosphere, taking in carbon dioxide from the air for photosynthesis. Cosmic ray protons blast nuclei in the upper atmosphere, producing neutrons which in turn bombard nitrogen, the major constituent of the atmosphere . This neutron bombardment produces the radioactive isotope carbon-14. carbon- The radioactive carbon-14 combines with carbon- oxygen to form carbon dioxide and is incorporated into the cycle of living things.The carbon-14 forms at a rate which appears to be constant, so that by carbon-measuring the radioactive emissions from once-living matter and once-comparing its activity with the equilibrium level of living things, ameasurement of the time elapsed can be made. made.
  • Radioactive Dating Radioactive half-life of a given radioisotope is not affected half- by temperature, physical or chemical state, or any other influence of the environment outside the nucleus. nucleus.Radioactive samples continue to decay at a predictable rate. rate. This makes several types of radioactive dating feasible. feasible.There are two main uncertainties in the dating process: process: 1. What was the amount of the daughter element when the rocks were formed? 2. Have any of the parent or daughter atoms been added or removed during the process?
  • Balancing Nuclear Decay Equations 238 --------> 90Th234 + 2He4 92U Proton and nucleon counts ----------------------------------------- must Subscripts are "proton be the same: numbers" 92 = 90 + 2 Superscripts are "nucleon 238 = 234 + 4 numbers"Distribution of Energy in Alpha Emission ∆m = 0.0046 u E = 0.0046 x 931 = 4.3 MeV ----------------------- Which particle has the greater kinetic energy?
  • Energy Distribution in Radioactive Decay Conservation of momentum: Mv = mV (2) Rearranging, we get Ratio of kinetic energies: V/v = M/m (3)KEm / KEM: (1/2 mV2) / (1/2 Mv2) Substitute (3) into (1): = (m/M)(V2/v2) Ratio = (m/M)(M/m)2 (4) = M/m = (m/M)(V/v)2 (1) Smaller mass gets more energy
  • Smoke Detector Alpha particles emitted from source ionize the air and provide the charge necessary to conduct current through the air. Charges stick to the heavy smoke particles and the current drops, causing the alarm to buzz.
  • Wavelength of a Gamma RayWhat is the wavelength of a 1 MeV gamma ray?Using the 1234 rule:λ = 1234 eV-nm / E = 1234 eV-nm / 1 x 106 eV = 1.23 x 10-6 nm = 1.23 x 10-15 m = 1.23 fermiThis gamma radiation is extraordinarily harmfulto humans and other living things since itswavelength is comparable to the diameter ofa nucleon; transmutations are likely whensuch radiation reaches nuclei.
  • 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 1991
  • Calculating the Icemans Age The current activity per gram of carbon is 0.23 Bq per gram. Icemans carbon showed 0.121, or about half what it would be if the Iceman were alive. Since the half-life of carbon-14 is about 5700 years, the Icemans remains are about 5700 years old.
  • The Shroud of Turin Since the1354 AD, a yellowing piece of linen 14-ft long has been stored in Turin, Italy. It bears the image of a person who seems to be wearing a crown of thorns. Could the Shroud of Turin have been the burial cloth of a person who died two thousand years ago?
  • Dating of the Shroud of Turin At the time of the public exhibition of the shroud in 1354, a bishop declared it to be fraud. Most religious bodies take a neutral stance on the shrouds authenticity. In 1988, three laboratories were given four pieces of fabric; three were control pieces similar in appearance, and one was a piece from the shroud. The labs all agreed that the shroud was 608- 728 years old, which means that it came into existence sometime between1260 and 1380 AD, a time span which includes the year the shroud was first shown to the public.
  • In 1934, Irene and Frederic Joliot-Curie discover theartificial radioactivity, making a great step toward the useand the control of radioactivity. For this discovery, theyreceived the Nobel price of chemistry in 1935.They were the first to show that mankind could build undercontrol some news radioactive nuclei. By shooting analuminium sheet with alpha particles (helium nuclei), theywere able to make radioactive phosphorus, a new isotope ofthe stable phosphorus that was never observed in nature.They demonstrated it by chemically isolating the phosphorusproduced before it becomes silicium by its radioactivity. Thecreation an unnatural radioactive element is what we call thecreation of artificial radioactivity.
  • PositronsIn 1930 Paul Dirac calculated the existence of electrons with positive charges. These "anti-electrons" would beexpected to have the same mass as the electron, but opposite electric charge. In 1932 Carl Anderson was examiningtracks produced by cosmic rays in a cloud chamber. One particle made a track like an electron, but the curvature ofits path in the magnetic field showed that it was positively charged. He named this positive electron a positron. Weknow that the particle Anderson detected was the anti-electron predicted by Dirac. An electron and positronannihilate one another producing two gamma rays (β- + β+® γ + γ).Irene Curie-Joliot (1897-1956), the daughter of Marie & Pierre, and her husband Frédéric Joliot preparedphosphorus-30 by bombarding aluminum with alpha particles..Phosphorus-30 does not occur in nature and is radioactive. This was the first artificial radioactive substance everprepared. Aside from the three natural types of radioactivity (α,β,γ), artificially made nuclei can undergo:Both positron emission and electron capture tend to occur for radioactive isotopes that need to convert a proton intoa neutron. The Curie-Joliots were awarded the Nobel Prize in Chemistry in 1935 for discovering artificialradioactivity.
  • Chemical Reaction Nuclear reactionAtoms are rearranged by Elements (or isotopes ofthe breaking and formation the same elements) areof chemical bonds converted from one to anotherOnly electrons in atomic Protons, neutrons,orbitals are involved in the electrons and otherbreaking and forming of elementary particles maybonds be involvedAbsorption or release of Absorption or release ofsmall amounts of energy tremendous amounts of energyRates of reactions are Rates of reactions are NOTaffected by temperature, affected by temperature,pressure, concentration pressure, concentrationand catalysts and catalysts
  • Producing Radioactive Isotopes:TRANSMUTATION is the process of changing one elementinto another.A stable atom can be bombarded with fast-moving a particles,protons, or neutrons.A radioactive isotope is called a RADIOISOTOPE.
  • Half-Life:The HALF-LIFE of a radioisotope is the amount of time ittakes for half of the sample to decay.A DECAY CURVE is a graph of the decay of a radioisotope(amount vs. time).Some radioisotopes have long half-lives. For otherradioisotopes, the half-life can be short.
  • Radioactivity Penetrating power of different forms of radiation:The image cannot be display ed. Your computer may not hav e enough memory to open the image, or the image may hav e been corrupted. Restart y our computer, and then open the file again. If the red x still appears, y ou may hav e to delete the image and then insert it again.
  • Chemical reactions CH4 + 2O2 CO2 + 2H2O + some energyOne molecule or element reacts with another one. Get a rearrangement (different combination) of elements.No new elements are created (C, H, O before and C, H, O after)
  • – a nuclear reaction As an example, when uranium 238 emits an alpha particle, it loses 2 protons and 2 neutrons. 238 234 4 92 U −− > 90 Th + He 2– Nuclear reactions must balance just like any other chemical reaction, but we must also be aware of balancing protons and neutrons
  • Nuclear ReactionsNuclear reactions occur when a nucleus is struck by aparticle or other nucleus. n+ 14 N → 1 4C + p 7 6 4H e+ 14 N → 1 7O 1 + 1H 2 7 8•The second reaction was observed by Rutherford and is thefirst nuclear reaction observed.•It should be noted that in the first reaction, the neutron canenter the nucleus with very little energy but the 4He is repelledby the nucleus and thus has to overcome the Coulomb barrierin order to come close enough to cause a nuclear reaction.
  • Parameter Chemical Reaction Nuclear ReactionReaction H + H → H2 H + H → 2H (D)Mechanism Interaction of Interaction of nuclei electronsSpecies Do not change New species formEnergy ∆H = 104.2 kCal/mol Q = 33.47 x 106change 1.73 x 10-22 kCal.atom kCal/mol (4.5 eV/atom) 5.56 x 10-17 kCal/atom (1.452 MeV/atom)Conservatio Maintained Maintainedn of massand energy
  • Radioactivity in NatureOur world is radioactive and has been since it was createdOver 60 radionuclides (radioactive isotopes) can be found in nature.Radionuclides are found in air, water, food and soilRadionuclides are even found in our bodyEveryday we ingest and inhale radionuclidesIn addition to radionuclides found in natureWe haveCosmogenic radionuclides: formed as a result of cosmic ray interactionsMan-made radionuclidesNumber of radionuclides > 2000Number of elements: 111
  • Natural Radioactivity in soilHow much natural radioactivity is found in a volume of soil that is 2.6 sq KM, 30cm deep (total volume = 7.894 x 105 m3)Every day, we ingest/inhale nuclides in our air we breath, in the food we eatand the water we drink. Radioactivity is common in the rocks and soil thatmakes up our planet, in the water and oceans, and even in our buildingmaterials and homes. It is just everywhere. There is no where on Earth that youcan get away from Natural Radioactivity.Radioactive elements are often called radioactive isotopes or radionuclides.There are over 1,500 different radioactive nuclides
  • Natural Radioactivity in FoodFood 40K (pCi/kg) 226Ra (pCi/kg)Banana 3,520 1Carrot 3,400 0.6 - 2White potatoes 3,400 1 – 2.5Beer 390 ----Red meat 3,000 0.5Drinking water ----- 0 – 0.17 Handbook of radiation measurement and protection
  • Radionuclides in building materialsMaterial Uranium (µg/g) (µg/g) Thorium (µg/g) (µg/g) Potassium (µg/g) (µg/g)Granite 4.7 2 4Sandstone 0.45 1.7 1.4Cement 3.4 5.1 0.8Limestone 2.3 2.1 0.3concreteSandstone 0.8 2.1 1.3concreteDry 1 3 0.3wallboardByproduct 13.7 16.1 0.02gypsumNatural 1.1 1.8 0.5gypsumWood - - 11.3Clay brick 8.2 10.8 2.3
  • Some radionuclides in human bodyNuclide Total mass Total Daily of nuclide activity intake in the bodyUranium 90 µg 1.1 Bq 1.9 µgThorium 30 µg 0.11 Bq 3 µgPotassium- 17 mg 4.4 kBq 0.39 mg40Radium 31 pg 1.1 Bq 2.3 pgCarbon-14 95 µg 15 kBq 1.8 µgTritium 0.06 pg 23 Bq 0.003 pg