Slide 1 : Chapter Nuclear Physics Gaurav Arora 1 Nuclear Physics
Slide 2 : The phenomenon by virtue of which a substance spontaneously disintegrate by emitting certain radiations is called radioactivity. Radioactivity There are three basic types of decay : Modes of Decay 1. Beta (b) Decay (a) b– Decay (Electron Emission) : It is the phenomenon of emission of an electron from a radioactive nucleus. Electrons or b– radiation are emitted from the nucleus when a neutron is converted into a proton, an electron and anti neutrino. This reduces the N/P ratio. In b– decay, the mass number remains unchanged, but the nuclear charge increases by one unit. The Q value for b– decay is given by : Q = (MX – MY) c2 Gaurav Arora 2 Nuclear Physics
Slide 3 : (b) b+ Decay (Positron Emission) : It is the phenomenon of emission of a positron from a radioactive nucleus. In b+ decay, mass number remains same but atomic number decrease by one unit and the element moves one place to the left in the periodic table. Positron or b+ radiation (positive electrons) result from the transformation of a proton to a neutron. The positron is ejected from the nucleus together with an neutrino v. The Q value for b+ decay is given by Q = (MX – MY – 2me) c2 Gaurav Arora 3 Nuclear Physics
Slide 4 : (i) The energy spectrum of b-particle is continuous. In beta decay the disintegration energy is shared between the three decay products, the daughter nucleus, electron or positron and the anti-neutrino or neutrino. As consequence, the kinetic energy of an electron, or a positron in beta decay process is not unique, it may range from zero to a certain maximum Kmax (end point) as shown in figure. The maximum kinetic energy Kmax of an electron or positron is equal to the disintegration energy (Q-value). When the electron or positron carries the maximum energy, the energy carried by the daughter nucleus and the anti-neutrino or neutrino is approximately zero and vice-versa. (ii) The mass of neutron is larger than the mass of a proton, therefore an isolated proton does not decay to a neutron. On the other hand, an isolated neutron decays to a proton. (iii) Anti-neutrino or neutrino interact very weakly with mater and can even penetrate earth without being absorbed. Therefore, their detection is extremely difficult. Gaurav Arora 4 Nuclear Physics
Slide 5 : The final product after decay is a nucleus whose charge is Z – 1. ZXA + e– ¾® Z–1YA + v The Q value for electron capture is Q = (MX – MY) c2 This process increases the N/P ratio. Usually an electron from the shell closest to the nucleus is captured. This is called the K shell, so the process is called K-electron capture. Gaurav Arora 5 Nuclear Physics
Slide 6 : (a) Neutron Emission : This form of decay is rare and only takes place with highly energetic nuclei. This is because the binding energy of the neutron in the nucleus is high (about 8 MeV). Nucleon Emission (b) Proton Emission : Except for nuclei in a very high energy state, proton emission is unlikely as the energy needed to remove a proton is about 8 MeV. (c) Alpha Decay : It is the phenomenon of emission of an a-particle from a radioactive nucleus. When a nucleus emits an alpha particle, its mass number decreases by 4 and charge number decreases by 2. An alpha particle consists of two protons and two neutrons; or it is doubly ionised helium atom. Gaurav Arora 6 Nuclear Physics
Slide 7 : Gaurav Arora 7 Nuclear Physics
Slide 8 : It is the phenomenon of emission of gamma ray photon from radioactive nucleus. Electromagnetic Process (Gamma Decay) This occurs when an excited nucleus makes a transition to a state of lower energy. Generally the nucleons rearrange themselves quite rapidly thus lowering the energy of the daughter nucleus to the ground state, the corresponding amount of energy is emitted. This is in the range 0.1–1.5 MeV and is emitted as electromagnetic radiation of very short wavelength, called g rays. In gamma decay, neither the proton number not the neutron number changed. Only the quantum states of the nucleon changes. Gaurav Arora 8 Nuclear Physics
Slide 9 : (i) Radioactivity is due to the spontaneous disintegration of a nucleus. Laws of Radioactivity (ii) Rate of disintegration is not affected by the external conditions like temperature and pressure etc. (iii) Law of conservation of charge holds good in radioactivity. It means the total charge before disintegration and that after disintegration must be same. (iv) Radioactivity is a random process. This means we can’t talk about decay of a particular nucleus and its disintegration is a matter of change only. (v) Each of the product of disintegration is a new element having physical and chemical properties different from those of the parent atom. Gaurav Arora 9 Nuclear Physics
Slide 10 : Rate of disintegration of the radioactive substance, at any instant, is directly proportional to the number of atoms present at the instant. This is known as statistical law of radioactivity. Let ‘N’ be the number of atoms of a radioactive sample at any instant. If ‘dN’ is the number of atoms which get disintegrated in a small time ‘dt’, Gaurav Arora 10 Nuclear Physics
Slide 11 : The life time of a particular nucleus can be anything from 0 to ¥ where as life time of radioactive sample is infinite. Gaurav Arora 11 Nuclear Physics
Slide 12 : Half life of a radioactive substance is defined as the time during which the number of nuclei of the substance are-reduced to half their original value. Half Life – (T1/2) N = N0e–lt Gaurav Arora 12 Nuclear Physics
Slide 13 : The average life of an nucleus of radioactive substance is equal to the sum of life times of the nuclei divided by the total number of nuclei. Average Life (tAV) Gaurav Arora 13 Nuclear Physics
Slide 14 : The activity of a radioactive substance is defined as the rate of decay or the number of disintegration per second. Activity of Radioactive substance A = A0e–lt A0 = lN0 S.I. unit of activity is Becquerel (Bq) 1 Bq = 1 dps (decay per second) 1 curie (Ci) = 3.7 × 1010 disintegration/sec 1 rutherford (rd) = 1016 disintegration per second Gaurav Arora 14 Nuclear Physics
Slide 15 : In numerical problems, it is convenient to use following relation Important Point Probability of a nucleus for survival upto time ‘t’ is given by Probability of a nucleus to disintegration in time ‘t’ is given by p = 1 – e–lt One of the situation of interest is when radioactive nuclei are being produced at some constant rate P by nuclear reactions in an accelerator or a nuclear reactor. Gaurav Arora 15 Nuclear Physics
Slide 16 : The graph between N versus t is shown in figure. In producing radioactive isotopes, it clearly does not pay to extend the production period over more than a few half lives. Gaurav Arora 16 Nuclear Physics
Slide 17 : A 32P radionuclide with half life 14.3 days is produced in a reactor at a constant rate q = 2.7 × 109 per second. How soon after the beginning of production of radionuclide will its activity be equal to A = 1 × 109 disintegration/sec Example : In the reactor just after production of radio nuclide, it starts decaying. The accumulation rate of the ratio nuclide can be given as Solution : When activity l N = 1 × 109 dps then = 9.55 days Gaurav Arora 17 Nuclear Physics
Slide 18 : The mean lives of a radioactive substance are 1620 years and 405 years for a-emission and b-emission respectively. Find out the time during which three fourth of a sample will decay if it is decaying both of a-emission and b-emission simultaneously. Example : The decay constants for a and b emissions are 1/1620 and 1/405 per year respectively. In this case effective decay constant for both decays simultaneously is l = la + lb Gaurav Arora 18 Nuclear Physics
Slide 19 : Suppose a parent radioactive nucleus A (decay constant = la) has number of atoms N0 at time t = 0. After disintegration it converts into a nucleus B (decay constant = lb) which is further radioactive. Initially (t = 0), number of atoms of B are zero. We are interested in finding Nb, the number of atoms of B at time t. Successive disintegration At time t, net rate of formation of B = rate of disintegration of A – rate of disintegration of B. Gaurav Arora 19 Nuclear Physics
Slide 20 : Integrating, we get which c is the constant of integration, which can be found as under At time, t = 0, Nb=0 Substituting this value, we have Now following conclusions may be drawn from the above discussion. 1. From Eq. (ii) we can see that Nb = 0 at time t = 0 (it was given) and at t = ¥ (because B is also radioactive) Gaurav Arora 20 Nuclear Physics
Slide 21 : 2. Na will continuously decrease while Nb will first increase (until laNa > lbNb), reaches to a maximum value (when laNa = lbNb) and then decreases (when lbNb = laNa). The two graphs for Na and Nb with time are shown below : 3. From equation number (ii) it seems as if lb should be greater than la for this equation to hold good but it is not so. Because of lb > la then e–lat > e–lbt and Nb will be positive and if la > lb then e–lat < e–lbt and again Nb is positive. Gaurav Arora 21 Nuclear Physics