Fig.5. 1: Sign of radiation precaution.

    Key unit Competence 

    By the end of the unit, I should be able to analyze atomic nuclei and radioactivity decay 

    My goals 

    • Define atomic mass and atomic number 

    • Identify the constituents of a nucleus  

    • Explain Einstein’s mass-energy relation. 

    • Define nuclear fusion and fission. 

    • Analyze determinations of a mass of nuclei by using Bainbridge mass spectrometer. 

    • Derive the relationship between decay constant and half-life.  

    • Determine the stability of a nuclei. 

    • Describe properties of different radiations.  

    • Describe creation of artificial isotopes.  

    • Identify the application of radioactivity in life. 

    • Plot a graph of binding energy against nucleon and explain its features. 

    • Calculate the decay rate of unstable isotopes.  

    • Appreciate the safety precautions to be taken when handling radioactive materials.  

    • Appreciate that the nucleus of an atom and quantum system has discrete energy levels.

    Introductory activity: The uses of radiation


    In different places like industries, hospitals, and other sensitive places, there are different posts that caution someone about dangerous substances one may encounter if care is not taken. Among the reasons why these places bare such instruction is because of chemicals and radiations that are used in such places which may be harmful if not handled with care. 

    1. Discuss some of the safety signs you have ever seen in any hospitals or industry if you have ever visited one. 

    2. Why do you think there is a need to put those signs in such places? 

    3. It is believed that there are some of diseases that are treated using radioactive substances. Can you state some of the radiations used to treat some diseases. 

    4. There are natural men made radioactive substances. All of these are used for different purposes. What are some of negative effects of these radiations to (i) man , (ii) environment 

    5. Some countries like Iran are affected by these radiations. Imagine you were a resident of that country, what would you do to protect yourself from such effects of radioactive substances.


    5.1.1 Standard representation of the atomic nucleus 

    Activity 5.1: Investigating the stable and unstable nucleus 


                             Fig.5. 2 The standard representation of an atom nucleus 

    Observe the Fig.5.1 above of an atom and answer to the questions that follow: 

    1. What do numbers A and Z stand for? 

    2. Describe the relation between the two numbers and their meanings. 

    3. When do we say that an atom is stable or unstable? 

    4. Explain clearly the meaning of isotopes. Give an example of isotopes you know.

    A nucleus is composed of two types of particles: protons and neutrons. The only exception is the ordinary hydrogen nucleus, which is a single proton. We describe the atomic nucleus by the number of protons and neutrons it contains, using the following quantities:

    • The atomic number or the number of protons Z in the nucleus (sometimes called the charge number). 

    • The neutron number or the number of neutrons N in the nucleus. 

    • The mass number or the number of nucleons in the nucleus, 


    5.1.2 Classification

    Depending on the combinations of protons and neutrons in the nucleus, nuclides can be classified in the following 3 categories: 

    a. Isotopes: These are nuclei of a particular element that contain the same number of protons but different numbers of neutrons. Most elements have a few stable isotopes and several unstable, radioactive isotopes. 

    Therefore, the chemical properties of different isotopes of an element are identical but they will often have great differences in nuclear stability. For stable isotopes of light elements, the number of protons will be almost equal to the number of neutrons. Physical properties of different isotopes of the same element are different and therefore they cannot be separated by chemical methods i.e. only physics methods such as the centrifugation method can be used to separate different isotopes of an element. 

    b. Isobars: these are nuclei which have the same mass number but     different number of protons Z or neutrons N. 

    c. Isotones: these are nuclei in which the number of neutrons is the same but the mass number A and the atomic number Z differ

    5.1.3 Units and dimensions in nuclear physics 

    The standard SI units used to measure length, mass, energy etc. are too large to use conveniently on an atomic scale. Instead appropriate units are chosen. 

    • The length: The unit of length in nuclear physics is the femtometer.

    This unit is called Fermi in the honor of the Italian Americano physicists who did a lot of pioneering work in nuclear physics.

     • The mass: The unit used to measure the mass of an atom is called the atomic mass unit, abbreviated “amu or u” and is defined as a 1/12 the mass of an atom of carbon-12. Since mass in grams of one carbon-12 atom is its atomic mass 

    The time: the time involved in nuclear phenomena is of the order of 10-20s to million   or billion years. 

    Nuclear radius: various types of scattering experiments suggest that nuclei are roughly spherical and appear to have the same density. The data are summarized in the expression called Fermi model. 


    This high density can explain why ordinary particles cannot go through the nucleus as highlighted by Rutherford experiments. The same density was only observed in neutron stars. The nuclear mass can be determined using a mass spectrometer.

    5.1.4 Working principle a mass spectrometer

    The figure below highlights the working principle of a typical mass spectrometer used to separate charges of different masses. It can be used to differentiate isotopes of a certain element.


                                                           Fig.5. 3: Bainbridge mass spectrometer

    Ions are formed in ionization chamber and accelerated towards the cathode. The beam passes through the cathode and is focused by the collimating slits S1 and S2. The beam is then passed through a velocity selector in which electric and magnetic fields are applied perpendicular to each other. The ion moves in straight line path for which both the forces acting on it are equal         

                                                               qE=qvB                                                        (5.04) 

    The velocity of ion which passes un-deflected through the velocity selector is then given by 

                                                                v=E/B                                                          (5.05) 

    The ions then reach the vacuum chamber where they are affected by the magnetic field (B'B' ) alone and then move in circular paths; the lighter ions having the larger path radius. If the mass of an ion is m, its charge q and its velocity v then

                                                                qvB'=mv2/R                                                            (5.06)
                                                                R=mv/qB'                                                                (5.07) 

    The radius of the path in the deflection chamber is directly proportional to the mass of the ion. The detection is done by photographic plate when the ions fall on it. The fig. 5.5 shows the recorded mass spectrum for a gas containing three isotopes. Note the wider line for the mass m1, showing its relatively greater abundance.


                          Fig.5. 4: A recorded mass spectrum of a gas containing 3 isotopes




    5.2.1 Mass defect 

    Activity 5.2 Select the words in the following puzzle

    Observe the puzzle below. 

    1. Discover 8 different words related to particle Physics hidden in the puzzle below, and write them in your notebook. 

    2. Use them to formulate a meaningful sentence


    3. Complete  the sentences below using the words you discovered in the puzzle 

        a. An …….is the SI unit of energy.

        b. On the atomic scale, the ………..is not the SI unit of mass. 

        c. The ………..of nucleons is greater than the mass of a nucleus. 

        d. The atom releases ………when its nucleus is formed from its constituent particles 

        e. The binding energy per nucleon gives an indication of the …………of the nucleus. 

        f. The surprising suggestion that energy and mass are equivalent was made by ……in 1905. 

    4. Discuss and explain the meaning of the following expression as used in physics           

        a.Mass defect


        b.Biding energy

        d.Stable nuclides 

    The nucleus is composed of protons that are positively charged and neutrons that are neutral. The question is what is holding these particles together in this tiny space? 

    Experiences have demonstrated that the mass of a nucleus as a whole is always less than the sum of the individual masses of protons and neutrons composing that nucleus. 


    5.2.2 Einstein mass-energy relation

    In 1905, while developing his special theory of relativity, Einstein made the surprising suggestion that energy and mass are equivalent. He predicted that if the energy of a body changes by an amount of energy E, its mass changes by an amount m given by the equation

                                                                           E=mc2                                                       (5.02) 

    Where c is the speed of light and m mass of a body Everyday examples of energy gain are much too small to produce detectable changes of mass.



    Activity 5.3: Investigating radioactivity

    During the World War II, its final stage was marked by the atomic bombing on Nagasaki and Hiroshima towns in Japan (Fig.5.7). Observe the image and read the text provided below before answering the following questions.


    In August 1945, after four years of world war, united States B-29 bomber, dropped the atomic bomb over the cities of Hiroshima on August 6th 1945. 70.000 people died in 9 seconds, and the city of Hiroshima was leveled. 3 days after as second bomb was dropped in Nagasaki, Japan with the same devastating results. The bombing killed over 129.000 people. 

    The bomb released cataclysmic load of energy. The ones who were close enough to see the blast lost their eyes. It was the last thing they ever saw. The bright light of what the blinded them. The black of their eyes, the retina, melted away. The radiation received by the body is equivalent today’s thousands of x-rays. The human body can’t absorb unlimited radiation. It falls apart because the cells are dying of radiation poisoning, if the radiation is intense enough, it looks like a urn. Layers of the skin begin to fall off. The body vital functioning began to slow down until it stops.

    1. Describe and discuss the phenomena happening on two images. 

    2. From the text, show that the atomic bomb of Hiroshima was very harmful to human body. 

    3. What are the types of radiations should be there? 

    4. Stable isotopes do not emit radiations. What is the name of materials which emit radiations? Describe them. 

    5. What are the possible main radioisotopes used to produce energy in figure above? 

    6. Which processes are used to generate such heavy energy? Describe any one of your choice

    Radioactivity is one of the dynamic properties of nuclei, in this process the system makes a transition from a high energy state to a low energy by emitting α and β-particles or γ-rays. This process happens naturally and is not affected by any external agent such as pressure, temperature or electric and magnetic fields. The α-particles are Helium nuclei and can be stopped by a piece of paper while β-particles are either electron or positron. There are high energetic particles and can pass through one cm thick aluminum sheet. γ-rays are electromagnetic radiations and can be stopped by several inches of lead.

    5.3.1 Radioactive decay of a single parent 

     If we consider the activity A of a radioactive sample which is the number of decay events in a unit time we obtain a similar expression for the radioactive decay law but expressed in terms of activity of the radioactive substance:


    5.3.2 Characteristics of radioactive substances

    Radioactive substances (nuclides) present one or more of the following features 

    • The atom of radioactive elements are continually decaying into simpler atoms as a result of emitting radiation 

    • The radiations from radioactive elements produce bright flashes of light when they strike certain compounds. The compound fluoresce. For example, rays from radium cause zinc sulphide to give off light in the dark.  For this reason, a mixture of radium and zinc sulphide is used to make luminous paints. 

    • They cause ionization of air molecules. The radiations from radioactive substances knock out electrons from molecules of air. This leaves the gas molecules with a positive charge. 

    • Radiations from radioactive substances can penetrate the heavy black wrapping around a photographic film. When the film is developed, it appears black where the radiations struck the film. 

    • Radiations from radioactive substances can destroy the germinating power of plants seeds, kill bacteria or burn or kill animals and plants. Radiations can also kill cancers.

    A. Properties of emitted radiations 

    Some of their properties are summarized and shown in the table below: 



    • A transmutation does not occur in gamma decay. When an alpha particles and beta particles are emitted, gamma rays are often emitted at the same time. When a radioisotope emits gamma rays, it become more stable because it loses energy. 

    • In both alpha and beta decay, the new element formed is called the daughter isotope.  

    • Gamma rays are like X-rays. Typical gamma rays are of a higher frequency and thus higher energy than X-rays.

    • Deviations of alpha, beta and gamma radiations due to electric field and magnetic field ( See Fig.5.9). It can be seen  unlike gamma-rays, alpha and  particles are affected by the presence of electric and magnetic fields since


    These reactions occur in the core of a star and are responsible for the outpouring of energy from the star. The sum of the exact masses of the helium atom is less than the sum of exact masses of the four hydrogen atoms. This lost mass is released as energy. It is thought that the sun’s energy is produced by nuclear fusion.

    5.3.4 Radiation detectors 

    Activity 5.4: Smoke detector bellow

    Observe the diagram of a smoke detector bellow then answer to the questions that follow:


    1. Name the components labeled A, B, C and D on the smoke detector above? 

    2. What is meant by smoke detector? 

    3. Describe a functioning of a smoke detector. 

    4. Design an inventory of other radiation detectors you know. Experiments in Nuclear and Particle Physics depend upon the detection of primary radiation/particle and that of the product particles if any. The detection is made possible by the interaction of nuclear radiation with atomic electrons directly or indirectly. 

    a. Classification of radiation detectors 

    There are a variety of other radioactive detectors that we may conveniently classify into two classes: Electrical and Optical detectors.


    Table5. 1 Classification of radiation detectors

    b. Working principle of an ionization chamber 

    Conventionally, the term “ionization chamber” is used exclusively to describe those detectors which collect all the charges created by direct ionization within the gas through the application of an electric field. Ionization chamber is filled with inert gases at low pressure. In the chamber there are two electrodes, namely, the cathode and the anode which are maintained at a high potential difference as shown on the figure below

     When radiation enters the chamber, it ionizes the gas atoms creating negative and positive charges. The negative charges or electrons are attracted by the anode while positive ions are attracted by the cathode; this produces the current in the outside circuit depending on the strength and the type of radiation. The current produced is quite small and dc amplified electrometers are used to measure such small currents.

    5.3.5 Checking my progress

    In the following exercises (1 to 4), choose the best answer and explain your choice 

    1. Which of the following is an electron?          

           a. Neutrino      

           c.  Photon

           b. Gamma particle

           d. Beta particle  
    2..Which of the following most accurately describe radioactive decay?

         a. Molecules spontaneously break apart to produce energy

         b. Atoms spontaneously break apart to produce energy beta decay, alpha decay and positron emission are all forms of radioactive decay. Energy is released because the atoms are converted to a more stable energy

         c. Protons and neutrons spontaneously break apart to produce energy

         d. Electrons spontaneously break apart to produce energy

    3. Which of the following is true concerning the ratio neutrons to protons in stable atoms?

        a. The ratio for all stable atoms is 1:1. 

        b. The ratio for small stable atoms is 1:1, and the ratio for large stable atom is greater than 1:1. As atomic weight goes up, the ratio of neutrons to protons for stable atoms increases up to as much as 1.8:1 ratio. 

        c. The ratio for large stable atom is 1:1, and the ratio for small stable atoms is greater than 1:1. 

        d. There is no correlation between the stability of the atom and its neutron to proton ratio.

    4. Polonium-218 undergoes one alpha decay and two beta decays to make 

            a. Polonium-214 

            c. Bismuth-214

            b. Plomb-214

            d. Plomb-210 

    5. a) Compare 

        (i) the charge possessed by alpha, beta and gamma radiations 

         (ii) The penetrating power of these radiations

    6. a.What is meant by the term

        (i) radioactive decay?

        (ii) Half-life of a radioactive substance?

     b. A 32 g sample of radioactive material was reduced to 2 g in 96 days. What is its halflife? 

        How much of it will remain after another 96 days? 

    7. 212Be Decays to 208Th by α-emission in 34% of the disintegration and to212Ra by β-emission in 66% of the disintegration. If the total half value period is 60.5 minutes, find the decay constants for alpha and beta and the total emission. 

    8. If a radioactive material initially contains 3.0milligrams of Uranium 234U  , how much it will contain after 150,000 years? What will be its activity at the end of this time? 


    Activity 5.5: Use of nuclear energy to generate electricity


                                                 Fig.5. 12: Nuclear power plant functioning mechanism diagram. 

    Many people disagree to the use of nuclear power to generate our electricity, even though the safety record of nuclear industry is extremely good. Observe clearly the image diagram of the nuclear power plant (Fig.5.13) and answer to the questions that follow

     1. Why do you think people disagree to the use of nuclear power station?

     2. What are the main parts of the power plant station observed in Fig.5.13?

     3. Analyze and explain the steps of energy transformation from reactor to generator

     4. Write a brief explanation on the advantages and disadvantages of using nuclear energy as a source of electricity if any

     5. Use internet and your library or any other resources to find out about the other application of radionuclides in our daily life

    People would not have fear of radiations when controlled in certain manner. Radioisotopes and nuclear power process have been used and produced improvement in various sectors. These includes: consumer products, food and agriculture, industry, medicine  and scientific research, transport, water resources and the environment. The following are some descriptive examples among others.

    5.4.1 Industry 

    Different materials we use at home are manufactured in industry and made of different radioactive materials. The dosage of use of radioactive substance is thus controlled so that they are not harmful to human body. 

    Gamma radiation and beta radiation from radio-isotopes can be used to monitor the level of the material inside the container. The penetrating power of gamma rays is used to detect hidden flow in metal castings. Beta rays are used to measure the thickness of various flat objects (the mass absorbed by the object is proportional to its thickness).

    In the textile industries, irradiation with beta radiations fixes various chemicals onto cotton fibers. This produces for instance permanent press clothing. Again, radioactive materials can be used as tracers to investigate the flow of liquids in chemical factories.


    If there is a sudden decrease in the amount of radiation reaching the detector, which will happen when the container is full, then this can be used as a signal to switch off the flow of substance into the container. A similar method is used to monitor the thickness of sheets of plastic, metal and paper in production.

    5.4.2 Tracer studies 

    Tracer techniques can be used to track where substances go to and where leaks may have occurred. Leaks in gas pipes or oil pipes can be detected by using this technique.

    Tracer techniques are also used in medicine to treat thyroid glands which can be underactive or over active. The activity of the thyroid gland can be monitored by the patient being injected with or asked to drink radioactive iodine. The radioactivity in the vicinity of the thyroid gland is then checked to see how much of the radioactive iodine has settled in the area around the gland.

    5.4.3 Nuclear power stations 

    Nuclear power stations control a large amounts of energy released when Uranium235undergoes nuclear fission. The energy released by this controlled chain reaction, is then used to produce electricity.

    5.4.4 Nuclear fusion

    In nuclear fusion, the nuclei of elements with a very low atomic number are fused together to make heavier elements. When this takes place, it is accompanied by a very large release of energy. In the sun, hydrogen nuclei are fusing together all the time to make helium nuclei.


                                                             Fig.5. 14: A gamma camera assembly. 

    The photons emitted in the patients are detected by the photomultiplier tubes. A computer monitor displays the image computed from the photomultiplier signals. 

     1. Who is this person (a man or a woman)?

     2. Where is he?

     3. What does the image on the right represent?

     4. What do you think the patient is suffering from?

     5. Using the knowledge acquired in optics, what kind of light propagation observed there?

     6. Does the imaging use reflection or refraction? Why?

     7.  What should be the name of radiation being used in this imaging?

    5.4.8 Agricultural uses

    In agriculture, radionuclides are used as tracers for studying plants, insect and animals. For example, phosphorus-32 can be added to plant fertilizer.  Phosphorus is absorbed by plants and its distribution can be measured. 

    Radiation has been used in South American to detect and control the screw worm fly pest. A large number of the male of the species were exposed to gamma radiation. When the males were released back into the wild and mated with wild females, sterile eggs resulted and no new flies were born. 

    The points of photosynthesis in a leaf are revealed by growing it in air containing carbon-14. The presence of this radioactive nuclide in the leaf is the revealed by putting the leaf onto a photographic plate and letting it take its own picture.

    5.4.9 Checking my progress 

     1. Suggest different uses of radionuclides in (i) Medicine (ii) food and agriculture

     2. In our daily life, we are exposed to radiations of different types mainly in materials we use.

         a. Make an inventory of all of the devices in your home that may have (contain) a radioactive substance

       . b. What is the origin of these radiations in the materials highlighted above?

         c. Explain the purpose of radioactive material in the device.

         d. Then make research to find out how the objects shown inFig.5.15 use radiation in their manufacture.


                                                                                        Fig.5. 15


    Activity 5.8: Investigating the safety in a place with radiations

                         Fig.5. 16: Radiation effects on human body according to the exposure. 

    The image above (Fig.5.16) shows different side effects of radiation on human body according to the exposure time taken. With reference to section 5.3 and activity 5.3, answer to the following questions:

      1. What are the dangers of radiations you may observe?

      2. Analyze measures should be taken for radiation users?

    5.5.1 Dangers of radioactivity 

           • Both beta particles and gamma rays can pass easily in the skin and can easily destroy or even kill cells, causing illness.

           • They can cause mutations in a cell’s DNA, which means that it cannot reproduce properly, which may lead to diseases such as cancer.

            • Alpha particles cannot pass through the skin. However, they are extremely dangerous when they get inside your body. This can happen if you inhale radioactive material.

    5.5.2 Safety precautions when Handling Radiations 

    The precautions taken by workers who deal with radioactive materials are:

     • Wearing protective suits

     • Wearing radiation level badges

     • Checking the radiation level regularly

     • Using thick lead-walled containers for transporting radioactive materials

     • Using remote control equipment from behind thick glass or lead walls to handle radioactive material

     • They should be held with forceps and never touched with hands.

     • No eating, drinking or smoking where radioactive materials are in use

     • Wash your hands thoroughly after exposure of to any radioactive materials

     • Any cuts in the body should be covered before using radioactive sources

     • Arrange the source during experiments such that the radiation window points away from your body

     • There are ten golden rules for working safely with radioactivity.



                                                                    Table 5. 5

    5.6.1 Multiple choice questions

    5.6.1 Multiple choice questions 

    Instructions: Write number 1 to 5 in your notebook. Beside each number, write the letter corresponding to the best choice 

     1. Radionuclides 

        a. Are those nuclides having more neutrons than protons

        b. May emit X-rays.

        c. Decay exponentially

        d. May be produced in a cyclotron

     2. Concerning Compton Effect:

        a. There is interaction between a photon and a free electron.

        b. The larger the angle through which the photon is scatted, the more energy it loses. 

        c. The wavelength change produced depends upon the scattering material.

        d. High energy radiation is scatted more than lower energy radiations.

        e. The amount of scattering that occurs depends on the electron density of the scattering material. 

    3. Classical physics offered a satisfactory explanation for 

        a. The diffraction of electrons by crystals 

        b. The deflection of charged particles in an electric 

        c. The intensity spectrum of black body radiation

        d. The photoelectric effect e. Matter waves 

    4. When investigating β decay, the neutrino was postulated to explain 

        a. Conservation of the number of nucleons

        b. Counteracting the ionizing effect of radiation

        c. Conservation of energy and momentum

        d. The production of antiparticles 

        e. The energy to carry away the β particles.

    5. Gamma radiations differ from α and β emissions in that 

       a. It consist in photons rather than particles having nonzero rest mass

       b. It has almost no penetrating ability 

       c. Energy is not conserved in the nuclear decays producing it 

       d. Momentum is not conserved in the nuclear decays producing it 

       e. It is not produced in the nucleus

    6. The process represented by the nuclear equation  is     

    a. Annihilation   c. β decay         e. γ decay               b. α decay   d. pair production

    7. Write number (i) to (iii) in your note book. Indicate beside each number whether the corresponding statement is true (T) or false (F). If it is false, write a corrected version. 

      I. An alpha particle is also called a hydrogen nucleus

      II. The neutrino was suggested to resolve the problem of conserving energy and momentum in β decay.

      III. The amount of energy released in a particular α or β decay is found by determining the mass difference between the products and the parent. A mass-energy equivalence calculation then gives the energy.

      IV. The average biding energy per nucleon decreases with the increasing atomic mass number

    8. A radioactive source emits radiations alpha, beta and gamma a shown below:


                                          Fig.5. 17 Absorption of radiation 

               The main radiation(s) in the beam at X and Y are