AL Physics/Radioactivity/P.1 PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Seven AL Physics Radioactivity Radioactivity Properties of α, β and γ radiations Detectors Random nature of decay Natural nuclear transformation Exponential law of decay. Half-life. The Becquerel. Radiation hazards Isotopes Mass, charge, energy, relative ranges in air and other materials, relative ionizing power. Familiarity with cloud chamber tracks assumed from lower level work. Structure and use of (i) an ionization chamber (ii) one type of cloud chamber (iii) the Geiger- Müller counter (count-voltage characteristic and details of scaler not required). Suitability of these detectors for α, β and γ emissions. dn/dt = -kn derived from analogy with dice decay. Interpretation of decay constant k as the constant chance of an atom decaying per unit time. Change of N and in radioactive decay (details of radioactive series not required). N = N exp(-kt). Relationship between k and t 1/2. Relevance of long half-lives to the disposal of radioactive waste and to radioactive fallout. Carbon-14 dating. Sources of background radiation and typical radiation doses. Hazards due to open and sealed sources. Handling precautions. The uses of radioisotopes (briefly). E48. Magnetic deflection of β rays (NAP 5.1/F1). E49. The penetrating power of α, β and γ rays (qualitatively). E5. Radioactive decay analogue (NAP 5.11/F 8) E51. Demonstration of random variation of count rate using G.M. counter and source. A. α, β and γ radiations a. - α-decay: In large nuclei (A > 2), the nuclei are very unstable. They try to increase their stability by reducing their mass. In the decay a helium nucleus, i.e. the α- particle, is emitted. So in α decay, the parent nucleus loses two protons and two neutrons. A A 4 X Y+ 2 4 2α - β-decay: A neutron by itself is unstable. It decays into a proton plus an electron. In a nucleus, one of the neutrons decays into a proton and an electron, i.e. the β- particle is emitted. So in β-decay, the mass number A is unchanged but increases by 1. A A X Y+ + 1 1β ** Indeed, in β-decay a neutrino is also emitted. - γ-decay: After the emission of α or β-particle, the nucleus is left in an excited state and may have a lot of energy. In order to get rid of this extra energy, photon, i.e. the γ ray, is emitted by the nucleus. A A X * Y+ γ
AL Physics/Radioactivity/P.2 b. Properties α β γ Nature Helium nucleus, 4 2 He electron photon Mass mass number = 4 electron mass Charge +2-1 Energy 4 to 1 MeV.25 to 3.2 MeV ~ 1 MeV Speed 5 to 7% of the speed of light 99% of the speed of light speed of light Relative ranges in air and other materials Relative ionizing power - a few centimeters in air - stopped by a thick sheet of paper - several meters in air - a few millimeters of aluminum - Several centimeters of lead Strong Medium Weak B. Nuclear radiation detectors 1. Ionization Chamber - Two electrodes, one electrode of the chamber is often a cylindrical can and the other a metal rod along the axis of cylinder. - Between the electrodes, electrons and positive ions are produced from neutral gas atoms by ionizing radiation from a source inside or outside the chamber. - Under the influence of an electric field between the electrodes, electrons move to the anode and positive gas ions to the cathode to form an ionization current. - The intensity of the radiation can hence be measured. - The current depends on the ionizing power of the radiation. For alpha source, a current of the order of 1-1 A can be creates, while beta particles and particularly gamma rays cause very much smaller currents. Ionization chamber Sensitive current detector 2. Geiger-Müller (G-M) tube a. Structure: protective gauze argon (+ halogen gas) anode R +V to amplifier and counter thin mica end window cathode - It consists of a cylindrical metal cathode (the wall of the tube) and a coaxial wire anode, containing argon at low pressure.
AL Physics/Radioactivity/P.3 - A very thin mica end-window allows the radiation to enter. - A p.d. of about 45 V is maintained between anode and cathode and since, the anode is very thin, an intense electric field is created near it. b. Mechanism: - If an ionizing radiation passing through the tube, an ion-pair is produced from an argon atom. - The resulting electron is rapidly accelerated towards the anode. When the electron has sufficient energy, it creates more ion-pair. This process repeats itself until many electrons and ions are produced. - An avalanche of electrons spreads along the whole length of the wire, which absorbs them to produce a large pulse of anode current. - Every single pulse represents a radioactive ray entering the G-M tube. - This process take about a few tenths of a microsecond. - The number of pulse given in a certain time can be counted by an electronic counter (scalar or ratemeter) which is connected to the G-M tube. c. Further points: (i) - During the electron avalanche the heavy positive ion have been almost stationary round the anode. - After the avalanche has occurred they move towards the cathode under the action of the electric field, taking about 1 microseconds to reach it. - The positive ions would cause the emission of electrons from the cathode by bombardment. A second avalanche would follow, maintaining the discharge and creating confusion. - A small amount of a quenching agent (Bromine) is added to prevent this. (The positive ion energy is used to decompose the molecules of the quencher). (ii) - The G-M tube has a dead time of about 2 microseconds due to the time taken by the positive ions to travel towards the cathode. - Ionizing particles arriving within this period will not give separate pulses. - If radioactive substance emitted particles at regular intervals, a maximum of 5 pulses per second could be detected. (iii) Almost every beta particle that enter the G-M tube can be detected. By contrast, the detection efficiency for gamma rays is less than 1%. 3. Cloud chambers (Diffusion Cloud Chamber) - The upper compartment contains air which is at room temperature at the top and at about -78 ºC at the bottom due to the layer of dry ice in the lower compartment. - The felt ring at the top of the chamber is soaked with alcohol, which vaporizes in the warm upper region, diffuses downwards and is cooled. - At about 1 cm from the floor of the chamber, the alcohol vapor becomes saturated.
AL Physics/Radioactivity/P.4 - When ionizing radiation passes through the air containing saturated vapor, condensation of the vapor occurs on air ions created by the radiation. - The resulting white line of tiny liquid drops shows up as a track, which is the path of the ionizing radiation, in the chamber when suitably illuminated. - Alpha particles give bright, straight tracks. Very fast beta particles produce thin, straight tracks whilst those traveling more slowly give short, thicker, tortuous ones. Gamma rays cause electrons to be ejected from air molecules and give tracks which are due to these ejected electrons. alpha particle Beta particle gamma ray C. Exponential Law of Decay 1. Random nature of decay - In a radioactive source, nuclei disintegrate independently. - Radioactive decay is a random process, i.e. the disintegration obey the statistical law of chance. We cannot tell which particular atom is going to disintegrate. We can only talk about the probability that the atom will decay in certain time interval.
AL Physics/Radioactivity/P.5 2. Exponential law of decay -Let k (radioactivity decay constant) be the probability that a nucleus will decay in unit time. - The number of nuclear disintegration per second, dn/dt, (define as the activity, unit: 1 becquerel = 1 disintegration per second, symbol Bq) is directly proportional to the number of radioactive nuclei, N, present at that instant. dn - Hence, = kn dt - Where the negative sign indicates that N decreases 1 with time t. Fraction of active nuclei N dn t - By integration, = k N N dt 1/2 N [ ln N] N = -kt - Hence, N = Ne kt 1/4 1/8 1/16 - Thus the number N of undecayed nuclei left decreases exponentially with the time t. ** By substituting N into the original differential equation, we have the activity dn = kn e kt dt Hence the activity also decreases exponentially with the time t. 1 2 3 4 Number of half-lives 3. Half-life, t ½ - The half-life, t ½, of a radioactive element is defined as the time taken for the atoms to disintegrate to half their initial number. -If N is the initial number of atoms, from the exponential decay law N Ne kt 12 = / 2 hence, t ½ = (ln 2)/k =.693/k - The half-life varies considerably for different radioactive atoms. e.g. uranium, t ½ = 45 million years; radon, t ½ = 1 minute. 4. Example:- A small source of beta particles is placed on the axis of a Geiger-Müller tube and a few centimeters from the window of the tube. State and explain three reasons why the observed count rate is less than the disintegration rate of the source. A source, of which the half-life is 13 days, contains initially 1. 1 2 radioactive atoms, and the energy released per disintegration is 8. 1-13 J. Calculate (a) the activity of the source after 26 days have elapsed and (b) the total energy released during this period.
AL Physics/Radioactivity/P.6 5. Carbon dating - Carbon has a radioactive isotope 14 C (half-live ~ 56 years). It is formed when neutrons react with nitrogen in the air. 14 1 14 1 N+ n C+ H 7 6 (The neutrons are produced by cosmic rays which interact with the air molecules in the upper atmosphere.) - The radioactive isotope 14 C is absorbed by living material such as plants in the form of carbon dioxide. Experiment shows that the activity of 14 C in living materials is about 19 counts per minute per gram. - When the plant dies, no more 14 C is absorbed. Activity of 14 C in the dead plant decreases exponentially. Measuring the activity of the isotope in the dead plant can provide information about its age, Carbon Dating. - Example:- If the measured activity A in a piece of ancient wood is 14 counts per minute per gram. Find the age of the ancient wood. The radioactivity decay constant, k, of 14 C = (ln 2)/t ½ =.693/56 year Then from A = A exp(-kt), we have 14 = 19 exp(-kt) hence, t = 2456 years 1 D. Radiation Hazards 1. - Dose equivalent H is a measure of the effect that a certain dose of a particular kind of ionizing radiation has on a person. It takes into account the type of radiation as well as the amount of energy absorbed. The unit of H is the sievert (Sv). - There are two major sources of radiation: natural radiation and artificial radiation. (i) Natural radiation: Cosmic rays from outer space, naturally occurring radioactive materials that exist in food, the air and our natural habitat. (ii) Artificial radiation: Medical practices (diagnostic X-rays), fallout of radioactive substances as a result of testing of nuclear weapons in the atmosphere, luminous watches, color TV, ionization chamber smoke detectors, etc. - The annual dose received by a member of the public in Hong Kong from natural background radiation is about 2 msv. The dose for radiation workers must not exceed 5 msv in a year and 5 msv per year for the general public above natural background. Death occurs with doses over 5 msv. Sickness is caused above 1 msv. Dose from a chest X-ray is roughly.3 msv. 2. - Radiation can cause immediate damage to tissue and is accompanied by radiation burns (i.e. redness of the skin followed by blistering and sores which are slow to heal), radiation sickness, loss of hair and, in extremely severe cases, by death. - Delayed effect such as cancer, leukemia and eye cataracts may appear many years later. - Hereditary defects may also occur in succeeding generations due to genetic damage.
AL Physics/Radioactivity/P.7 3. - Sealed sources should be (i) lifted with forceps, (ii) held so that the open window is directed away from the body and (iii) never brought close to the eyes for inspection. - For unsealed sources, gloves and masks should be used. E. Use of Radioisotopes - The extent to which radiation is absorbed when passing through matter depends on the material s thickness and density. In the manufacture of paper the thickness can be checked by having a beta source below the paper and a G-M tube and counter above it. - Level indicators depend on absorption and are used to check the filling of toothpaste tubes and packets of detergents. - Leaks can be detected in underground pipe-lines carrying water, oil, etc., by adding a little radioactivity solution to the liquid being pumped. Temporary activity gathers in the soil around the leak which can be detected from the ground above. - Gamma rays from high-activity cobalt-6 sources are used in radiotherapy in the treatment of cancer. - Medical instruments and bandages are sterilized after packing by brief exposure to gamma rays. Food may be similarly treated to stay fresh for a longer time.