A researcher has 500 MBq of 32 P but cannot use it for 35 days. What is the activity when she wants to use the material? T ½ = 14.3 days A = A o 2 n A = 91.7 MBq A = A o e t / T 1/2 example

3 Example Cobeta decay with a half-life of 5.27years=1.66x10 8 s into 60 Ni which then promptly emits two gamma ray, what is mass of 1000Ci cobalt source?

example What is the molar activity of 13 N, which has a half life of 9.96 minutes? Answer minutes = 598s A = x x /598 = 6.98 x disintegrations mol -1 s -1 (or Bq mol -1 ) or 6.98 x /3.70 x = 1.88 x Ci mol -1 4 For one mole number of atoms = Avogadro's numbers

Substance E has a half-life of 3 hours. If at 8 am it has a count rate of 600 per second, what will be its count rate at 2 pm? at 8 am count rate = 600 per second 2 pm is 6 hours later this is 2 half-lives later therefore the count rate will halve twice that is: 600  300  150 count rate at 2 pm = 150 per second A = A o e t / T 1/2 A=600 e x 6 / 3 example

A= N A g sample of 248 Cm has a alpha activity of mCi. – What is the half-life of 248 Cm? Find A – x Ci (3.7 x Bq/Ci)=2.35 x 10 7 Bq Find N N= m N A / A –.150 g x 1 mole/248 g x 6.02 x /mole= 3.64 x atoms  A/N= 2.35 x 10 7 Bq/3.64 x atoms=6.46 x s -1 – t 1/2 =ln2/  6.46E-14 s -1 =1.07E13 s – 1.07 x s=1.79E11 min=2.99E9 h=1.24E8 d =3.4E5 a example

If you have 1 gm of pure potassium 40 ( 40 K) that is experimentally determined to emit about 10 5 beta rays per second A- what is the decay constant? B-Estimate the half life of 40 K Solution :- A = λ N = λ x(mass/ mass number )x Avogadro, s number 10 5 = λ x 1/40 x 6.02 x So λ=6.7 x sec -1 T 1/2 = / λ = / 6.7 x = sec T 1/2 = 10 7 /3.15 x 10 7 =3 x 10 9 years example

The reaction is: What element results when 14 C undergoes beta decay? 1) 1) 15 C 2) 2) 15 N 3) 3) 14 C 4) 14 N 5) 15 O n  p + e - + changing a neutron into a protonZ increases by 1 Inside the nucleus, the reaction n  p + e - + has occurred, changing a neutron into a proton, so the atomic number Z increases by 1. However the mass number (A = 14) stays the same. : How would you turn 14 C into 15 N? example

shorter half-lifedecays more quicklyhigher activity If a sample has a shorter half-life, this means that it decays more quickly (larger decay constant ) and therefore has a higher activity: that is sample A. In this case, that is sample A. You have 10 kg each of a radioactive sample A with a half-life of 100 years, and another sample B with a half-life of 1000 years. Which sample has the higher activity? 1) sample A 2) sample B 3) both the same 4) impossible to tell  N/  t = – N : What is the ratio of activities for the two samples? example

larger activitydecays more quicklyshorter half-life A larger activity means that a sample decays more quickly, and this implies a shorter half-life. The same amount of two different radioactive samples A and B is prepared. If the initial activity of sample A is 5 times larger than that of sample B, how do their half-lives compare? 1) T 1/2 of A is 5 times larger than B 2) half-lives are the same 3) T 1/2 of A is 5 times smaller than B example

31-1 Interaction of Radiation with Matter  Radiation deposits small amounts of energy, or "heat" in matter  alters atoms  changes molecules  damage cells & DNA  similar effects may occur from chemicals  Much of the resulting damage is from the production of ion pairs

Natural Background Radiation Cosmic – Sun (much of this radiation is shielded by Earth’s atmosphere) Terrestrial Sources – Materials in soil – Break down into radon gas Radioactivity in the Body – Very minute quantities 12

Sources of Radiation Exposure in the U.S. Population Man Made (11%) - Medical X-rays CT scans - Nuclear medicine/ radiation oncology - Consumer products - Other 13

Direct Ionization Caused By: Protons Alpha Particles Beta Particles Positron Particles Indirect Ionization Caused By: Neutrons Gamma Rays X-Rays Energetic charged particles interact with matter by electrical forces and lose kinetic energy via: Excitation Ionization (The process of removing electrons from neutral atoms)

Non-Ionizing Radiation Radiation that doesn’t have the amount of energy needed to ionize the atom with which it interacts Examples: - radar waves- infrared radiation - microwaves- ultraviolet radiation - visible light

16 Ionization of atom or molecules by ionizing radiation Ionization of an atom results from the collision of radiation with the electron structure of an atom. Ionization occurs only when there is sufficient energy from the radiation to completely remove an electron from its orbit. The energy must therfore be larger than the binding energy of the particular orbital electron

Ionizing Radiation Positive ions,such alpha Particles, protons  Have very short range in matter roughly speaking Average range or stopping distance α 1/density of the medium – Heaviest and most highly charged ionizing radiations – Energy is used up quickly; low penetrating ability, Unable to penetrate skin, do not penetrate the dead layer of skin – Cannot travel more than 4 cm in air – Stopped by a thin layer of paper or clothing – Not a serious hazard outside the body Can be most damaging if inside the body (e.g., ingestion, inhalation) – Much more massive than an electron,so its path is nearly a straight line – Not all alpha travel same distance before stopping 17

α-particles are relatively large particles, thus they have lots of collisions with atomic electros of the materials through which they pass. During these collisions the α-particles energy can cause ionisation of the materials. α- particles cause lots of ionisation. about 100eV is transferred in a single collision,so many collision occur as the alpha slows  When its K.E decreases to 1MeV the alpha acquire 2 electrons and becomes a neutral helium atom.the neutral helium atom Comes to rest in a short distance after a few more collisions.  Very destructive once it gets into the body (e.g. inhalation or ingestion, or through a wound) due to its high linear energy transfer An internal hazard if swallowed,  the emitted alpha particles can cause ionization that results in damage to tissue 18

Energy loss Rate why α have a short range compared to electrons of the same energy? An ion traveling through a medium collides repeatedly with atomic electrons and gradually loses energy.The energy ΔK lost per unit distance by an ion with charge q and velocity v is ; ΔK α -q 2 /v 2 (the minus sign indicate that the ion is losing K.E ) ΔK is K.E lost per unit distance K ion =(1/2) mv 2 (v << c) (m is the mass of the ion) v 2 =2k/m ΔK α - mq 2 /2K ΔK α m so that massive particles such as alphas lose energy rapidly and come to rest in a short distance. 19

20 example Compare the rates of energy loss in a given material for protons and alpha having the same initial kinetic energies assuming v << C

Electrons and Positrons  These products of nuclear beta decays have ranges that are typically a hundred times greater than those of alpha particles. For example, a 1 MeV electron has a range in water or soft tissues of 0.4 cm.Like positive ions, electrons lose energy mainly by ionizing or exciting atoms.  For a given K.E the velocity will be much larger than for a proton or an alpha. (m e << m p )  A large deflection occurs in each collision with an atomic electron. So the electrons do not travel in a straight line The range of positrons the same as that  Electron and comes close to an electron  So that producing gamma rays Average range of electrons in water, aluminum, and lead. The range of alpha particles in water is shown again for comparison. 21

Photons  Gamma rays and X rays are both elec-tromagnetic quanta or photons,  but since the gamma rays originate in nuclear rather than atomic processes, they typically have more energy.  Photons do not produce appreciable ionization directly; instead, they lose energy to electrons that, in turn, cause ionization.  Consequently, photons have a long range in matter. For example, a 1-MeV photon in water has a mean range of roughly 10 cm.  Photon transfer energy to electron by three processes  At energy below 0.1 MeV, the photoelectric effect is most important { photon is absorbed by an atom, and an atomic electron is ejected. (for inner shell electrons and for atoms with large atomic number )}. 22 Electron out Photon in M to L L to K -

 At about 1MeV,Compton scattering dominates, photon – electron scattering,with transferring some but not all of its energy to an atomic electron  Pair Production for higher energies its possible for a photon to produce an electron – positron pair (occur near a nucleus when the photon energy is greater than the total mass energy of the two particles 2m e c 2 = 1.02MeV ) ~ ~ + ~ - + Electron out (recoil electron) Photon in Photon out -

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Neutrons; Neutrons are uncharged  produce ionization only indirectly.  Since they interact primarily with the small atomic nuclei rather than the atomic electrons, they have a very long range in matter.  Neutrons with energies of a few million electron volts may travel a meter or so in water or in animal tissues  Slowed by elastic scattering from nuclei and by nuclear reaction. Some of these reaction lead to proton or Gamma ray emission the proton causing biological effects once a neutron has slowed to thermal energies less than 1 eV being captured by a nucleus and followed by Gamma ray emission 25 Inelastic Scattering Neutron Capture Neutrons can collide with atoms causing theme to eject electrons

They are able to travel many feet in concrete and thousands of feet in air. Thick layers of materials with lots of hydrogen in them (like water or concrete) are needed to shield against neutron radiation. Protective clothing provides no shielding from neutron radiation. Neutrons are not likely to be encountered except in the initial seconds of a nuclear criticality event. Neutron particles Neutrons Uncharged Able to penetrate most materials deeply Hazard inside nuclear reactors 26

31.2 Radiation Units There are four radiation measurements used in different applications 1. Source activity 2. Exposure 3. Absorbed dose 4. Biological equivalent dose Source activity A source activity ( A ) is the disintegration rate of a radioactive material or the rate of decrease in the number of radioactive nuclei present. We can not measure the number of nuclei directly, but we can measure the rate of disintegrations per unit time. The rate of disintegration A is |dN/dt| and can be obtained from the equation; 27

Activity and Half-Life Activity and Half-Life are related. Low activity (few disintegrations per second) = long half-life. High activity = short half-life N = n N A n number of moles Molar Activity, Specific Activity and Half-Life are both independent of the amount of radioactive material present in the sample. 28

Radiation Penetration Into Skin Exposure to alpha & beta from outside body is slight hazard Long periods of exposure can cause “heat burns” Significant hazard if ingested, inhaled or contaminates a wound  Since alpha and beta are not powerful enough to penetrate deeply, they are primarily a hazard only when ingested, inhaled or when in an open wound.  Beta particles can cause a nasty skin burn if exposed for a long enough period; and beta particles are extremely hazardous to the unprotected human eye.  Where gamma radiation can pass through a human with ease, and therefore interact with sensitive internal organs. 29

Exposure is a quantity describing how much ionization is produced (i.e., how many electrons are liberated) in air by gamma- or x-rays. The unit of exposure is the Roentgen or Coulombs/kg (in the SI system). 1 Roentgen = 2.58 x Coulombs of charge produced per kilogram of air. absorbed dose, The amount of energy absorbed per unit of absorbing material. (new units: Gray) Describes how much energy is deposited in a material by a beam of ionizing radiation to unit mass of absorbing tissue, and is not restricted to x-rays or gamma rays passing through air. The unit of absorbed dose is the rad or Gray (in the SI system). 1 rad = 0.o1joule of energy deposited in one kg of material 1 Gray = 100 rads = 1joule 1 roentgen exposure to X rays or gamma =1 rad, the absorbed dose is used with all kind of ionizing radiation Standard International (SI) unit: Coulomb/kilogram (C/kg) Traditional unit: roentgen ( R )1 R = 2.58x10 -4 C/kg

Different types of radiation may deposit the same amount of absorbed dose but produce different effects and different levels of damage. overall. Equivalent dose, is derived by multiplying the absorbed dose by a quality factor (QF) which depends on the type of radiation being measured. The unit of dose equivalent is the rem or Sieverts (Sv) (in the SI system). Dose equivalent = Absorbed dose x QF QF = 1 for gamma rays, x-rays and most beta particles QF = for neutrons, depending on energy QF = 20 for alpha emitters under conditions of internal exposure 1 Sievert = 100 rems Biological Quantities The absorbed dose refers to a physical effect: the transfer of energy to the material the effects of radiation on biological system depend on the type of radiation and its energy the Quality factor (QF) is defined by comparing its effects to those of standard kind of radiation which is usually taken to be 200kev X rays

Quality Factor (QF) The specific value that accounts for the ability of different types of ionizing radiation to cause varying degrees of biological damage – X-rays, gamma rays, & beta particles 1 – Neutrons & High energy proton 10 – Alpha Particles 20 The quality factor of any type of radiation is the number of rads of X-ray or gamma radiation that produces the same amount of biological damage as 1 rad of that type of radiation. (Obviously different types of radiation have different biological effects.)

Different types of radiation behave in different ways. In order to compare the amount of risk or biological change that occurs, quality factors are introduced. For example: The damage produced by 1 Gy of x-radiation is equal to that produced by 1 Gy of gamma radiation. Thus, gamma radiation has a quality factor of 1 or 1 Gy gramma rays x 1 =1 Sv. The damage produced by 20 Gy of x-radiation is equal to that from 1 Gy of alpha radiation. Alpha radiation has a quality factor of 20 or 1 Gy of alpha radiation x 20 = 20 Sv. Quality factors for other types of radiation are between 1 & 20. Quality factor (QF) radiationQF photon,  1 proton, neutron10 alpha20

Rem (Roentgen equivalent man: As stated above, the rem is the unit for measuring the special quantity called dose equivalent. The rem takes into account the energy absorbed (dose) and the relative biological effect on the body due to the different types if radiation (expressed as the "quality factor" of the radiation). It is therefore a measure of the relative harm or risk caused by a given dose of radiation when compared to any other doses of radiation of any type. Occupational radiation exposure is recorded in rems. The rem can be thought of as the unit of biological hazard. Biologically Equivalent dose = absorbed dose x quality factors Biologically Equivalent dose rem = absorbed dose rad x quality factors Biologically Equivalent dose (Sievert (Sv)) = absorbed dose Gray (Gy) x quality factors rem Roentgen Equivalent Man The unit of dose equivalent for any type of ionizing radiation absorbed by body tissue in terms of estimated biological effect - Unit of dose equivalent Dose in health record is in units of rem 1 rem = 1 Roentgen The dosage of an ionizing radiation that will cause the same biological effect as one roentgen of X ray or gamma ray exposure

35 Example A laboratory experiment in physics class uses 10microcurie 137 Cs Source each decay emits a0.66Mev gamma ray (a) How many decays occur per hour? (b) a 60 kg student standing nearby absorbs 10 percent of gamma rays.What is her absorbed dose in rads in hour © the quality factor is 0.8.find her biologically equivalent dose in rems

A cancer is irradiated with 1000 rads which a QF of 0.7 Find the exposure in roentgens and biological equivalent dose in rem solution For gamma rays dose equal to the exposure in roentgens =1000R The biological equivalent dose is =(0.7x1000) =700 rems Example

SI Radiation Protection Units Becquerel (Bq) for Curie – 1 Ci = 3.7 x Bq Gray (Gy) for rad – 1 Gy = 100 rad Sievert (Sv) for rem – 1 Sv = 100 rem Absorbed dose definition applies to all forms of ionizing radiation in any material.

Pair Production An electron and a positron are produced and the photon disappears – A positron is the antiparticle of the electron, same mass but opposite charge Energy, momentum, and charge must be conserved during the process The minimum energy required is 2m e = 1.02 MeV Pair Annihilation In pair annihilation, an electron-positron pair produces two photons – The inverse of pair production It is impossible to create a single photon – Momentum must be conserved