(半衰期)

(半衰期) Chapter 12. Nuclear Physics Chapter 12 Nuclear Physics ?12.1 The basic properties of nucleus In proceeding chapters we have frequently made use of the fact that every atom contains a massive, positively charged nucleus, much smaller than the overall dimensions of the atom but nevertheless containing most of the total mass of the atom. It is instructive to review the earliest experimental evidence for the existence of the nucleus. It is well known that an atom has a nucleus in the center of the atom. The most obvious feature of the atomic nucleus is its size, of the order of 20,000 to 200,000 times smaller than the atom itself. Although the “surface” of a nucleus is not a sharp boundary, experiments determined an approximate radius for each nucleus. The radius is found to depend on the mass, which in turn depends on the total number A of neutrons and protons, usually called mass number. 12.1.1 the structures of nucleus 1. The electrical charges of nucleus: Nucleus is composed of protons and neutrons. Proton has a portion of positive charge which is the same as the electronic charge and neutrons have no electronic charges. Nucleus has positive charges and it is rotated. Because of this, it has angular momentum and magnetic moment. The smallest unit of charges is the integer multiples of electronic charge. The total number of positive charges, the number of protons, is denoted by Z which is also celled the atomic number. 2.Nuclear masses: Mass of an atom includes the mass of electrons and the mass of nucleus. The unit of atomic masses is defined as the carbon atom’s mass divided by 12, denoted by u. As the mass of a proton or a neutron is very close to 1u, the atomic mass number A is equal to the total number of protons (Z) and neutrons (N). Therefore, (12.1) A,Z，N where Z is atomic number which is the number of electron and N is the number of neutrons in the atom. ,27 (12.2) Atomic mass unit (u),1.66054，10kg m,1.007277u m,1.008655u (12.3) pn 12.1.2 Nuclear properties 146 Medical Physics 1. The size and density of the nucleus: The radii of most nuclei are represented fairly well by the empirical equation 13 (12.4) r,rA0 -15r is an empirical constant 1.2×10m, the same size for all nuclei. The density of 0 nucleon could be found as follows: MMAm3m,, (12.5) ,,,,344V4,r330rrA,,033 Where m is the mass of a nuclear such as proton or neutron which is given as 1.67 ， -2710kg. So the density of the nuclear is ,273(1.67，10kg)173, ,,2.3，10kg/mn,153,4(1.2，10m) 2. Nuclear forces and nuclear energy levels: The force of making the protons and neutrons together is obviously not electromagnetic force as neutrons are charge free and it is not the gravitational force either. Experiments show that such a force is a special interaction force which is called nuclear force. The force has four properties: -15(1). It is a “short distance force” as its effective distance is about 10m and out of this range it reduces to zero sharply; (2). The force is the strongest force we have observed so far; (3) the force has a feature of saturation, the nucleus can interact only with its nearest neighbor; (4) the interaction of nuclear force does not depend on charged condition of nuclei. That is that interaction forces from n-n, n-p and p-p are almost the same. Nuclei are same as the atoms and they also have discrete energy levels (angular momentum and magnetic moment). Energy transmission can be also happened under the surrounding perturbations. 12.1.3. Nuclear binding energy and mass defect (亏损) Nucleus is composed of nucleons (核子) and its mass should be equal to the sum of the mass of all the individual nucleon composing the nucleus. If the masses of the nucleus, the proton and the neutron are denoted by m, m, m respectively, we xpn should have such an equation m,Z,m，(A,Z)m (12.6) xpn Unfortunately, the experiments show that the nucleus mass is less the sum on RHS of the above equation and the difference is ,m, called the mass defect. Relativity points 147 Chapter 12. Nuclear Physics out that if there is mass defect, there must have energy changes. The difference of energy and the difference of the mass has the following relation. 2 (12.7) ,E,(,m)c where (12.8) ,,,m,Zm，(A,Z)m,mpnx is the mass defect. DE is called the nuclear binding energy. Such an energy was emitted when the nucleus was created. The higher the binding energy is, the more condensed and the more stable the nucleus is. This is why the nuclei are stable. ?12.2 The decay type of the atomic nucleus A single nuclear species with same Z and N is called nuclide. Nuclide has two big classes. One of them is radioactive nuclide and the other is stable nuclide. The radioactive nuclide can emit particle rays and be changed into another nuclide. This phenomenon is regarded as nuclear decay. 1.,decay The heavy nucleus with its mass number A>209 could emit a particles. The decay process can be written as AA,44 (12.9) X,Y，,，QZZ,22 where X is parent or radioactive nucleus, Y is daughter nucleus, is Helium’s nucleus and Q is the decay energy. No nucleus with A greater than 209 is stable. The stability of nuclei can be understood qualitatively on the basis of the nature of the nuclear force and the competition between the attractive nuclear force and the repulsive electrical force. As pointed out previously, the nuclear force favors pairs of nucleons, and pairs of pairs. In the absence of electrical interactions, the most stable nuclei would be those having equal numbers of neutrons and protons, N = Z. The electrical repulsion shifts the balance to favor greater numbers of neutrons, but a nucleus with too many neutrons is unstable because not enough of them are paired with protons. A nucleus with too many protons has too much repulsive electrical interaction, compared with the attractive nuclear interaction, to be stable. 2. , decay ,Decay denotes the parent nucleus becomes another nucleus spontaneously with its mass number unchangeable. Of course this decay is a decay to emit an electron. Such a decay has three kinds of forms that can be described by the following equations: 148 Medical Physics AA-,,,,X,Y，，，QdecayZZ，1 AA，，,,, X,Y，，，Qdecay ZZ,1 AA-X，,,Y，,，QelectroncaptureZZ,1 3. , decay and inner transmission Most of the daughter nuclei after α or β decay are in excited state and release their energies in , rays, and then leave them in ground state. This phenomenon is called , decay. In this process, a , photon is emitted. The inner transmission is the above phenomenon but no , photon emission. The energy was transferred to the electrons outside the nucleus. ?12.3 The nuclear decay law • The decay law If a radioactive sample contains N radioactive nuclei at some instant, it is found that the number of nuclei, ,N, that decay in a small time interval ,t is proportional to N: (12.10) ,N,,,N,t Where , is called decay constant. The negative sign signifies that N decrease with time; the value of , for any isotope determines that rate for which that isotope will decay. The decay rate is defined as the number of decay per second. dN,NdN,,,,,N,,,dtlimdt,tN,t,0 dN,,,dt , lnN,,,t，C,,N the decay law is ,,t (12.11) N,Ne0 • The half-life (半衰期) t = T, N = N/2 0 So we have ,,T1N,Ne002 ,T,e,2 0.693, (12.12) T,ln2 , T,, The unit of half-life is minute, hour, day or year. • The radioactivity 149 Chapter 12. Nuclear Physics The radioactivity is defined as the nuclear number of decay in unit time. It is sometimes called radioactive intensity or decay rate or activity, denoted by I. dNd,,t,,t ，，I,,,,Ne,,Ne00dtdt ,,t (12.13) ,,N,Ie0 The units of radioactivity are initially in Becquerel (Bq). 1Bq = 1 decay / s (Bq = Becquerel) 10 1 Ci = 3.7 ，10 Bq (Ci = Curie) 46 = 3.7 ， 10 MBq (M=mega ~10) 9 = 3.7 ， 10 GBq (G=Giga ~ 10) -212 = 3.7 ， 10 TBq (T = Tera ~ 10) 3 = 10 mCi (millicurie) 6 = 10mCi (microcurie) (12.14) It is known that they are similar to meters used. Example 12-1: The activity of radium: the half-life of the radioactive nucleus 226316 is 1.6 ， 10 years. If the sample contain 3.0 ， 10 such nuclei, determine the Ra86 activity at this time. Solution: first, let us convert the half-life to seconds 37T,(1.6，10years)(3.15，10s/year) 10 ,5.05，10s So the decay constant can be obtained as: 0.6930.693,11,1 ,,,,1.4，10s10T5.05，10s We can calculate the activity of the sample at t = 0 using dN,t,,,I,,,Ne|,N0000,tdt 11116,, ,1.4，10s3.0，10，，，， 5 ,4.2，10Bq/s,11.1,Ci 150 Medical Physics ?12.4 Introduction to Elementary Particles 12. 4.1 The basic properties of particles • Masses, • Charges, • Spin, • Magnetic moment • Average life-time. 12. 4.2 The interactions between particles • Gravitational interaction, • Weak interaction, • Electromagnetic interaction, • Strong interaction • Unification of the four interactions 12. 4.3 The classification of particles • Photons • Leptons (轻子) and lepton numbers • Hadrons (强子): Any of a class of subatomic particles that are composed of quarks and take part in the strong interaction. 12.4.4 Vector Boson (矢量玻色子): Any of the elementary particles that mediate one of the four fundamental forces or interactions is called vector Boson. • Photon transmits the electromagnetic force, • Graviton transmits the gravitational force, • Intermediate vector boson transmits the weak interaction, and • Gluon transmits the strong interaction. Problems 161241. Try to explain that is impossible. O,C，He 242. Calculate the emitting energy for two H molecules combining one H molecule. 3. If the emitting energy of two hydrogen atoms combining one hydrogen molecules is 4.37 eV, try to calculate the mass defect due to this process. 4. Calculate the nuclear binding energy and the nuclear average binding energy for deuteron and helium? 131th5. The half-life of I (iodine) is 8.04d. If it is measured at 9:00 am on 12 when its 6thradioactivity was 5.610 Bq, how much will it be at 3:00 pm on 30 in the same month? 151 Chapter 12. Nuclear Physics 6. There are two kind of radioactive nuclides whose half-life are 8d and 6h respectively. Suppose that their radioactivities are the same, find the radio of the two radioactive nuclide numbers. 152 Medical Physics 153