# RADIOACTIVE DECAY. In this section, we describe radioactivity - how unstable nuclei can decay - and the laws governing radioactive decay.

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1 ctivity BP RDIOCTIVE DECY Section 8: RDIOCTIVE DECY In this section, we describe radioactivity - how unstable nuclei can decay - and the laws governing radioactive decay. Radioactive Decay Naturally occurring radioactive nuclei undergo a combination of α, β and γ emission. rtificially produced nuclei may also decay by spontaneous fission, neutron emission and even proton and heavy-ion emission. ny decay process is subject to the same basic law. RDIOCTIVE DECY LW The rate of decay (number of disintegrations per unit time) is proportional to N, the number of radioactive nuclei in the sample dn/dt N (6.1) The negative sign signifies that N is decreasing with time. is called the decay constant - probability per unit time that a given radioactive nucleus will decay. Large rapid decay; small slow decay. Equation (6.1) can be integrated to give N(t) = N 0 exp( t) (6.2) where N 0 = number of radioactive nuclei at t = 0. CTIVITY ND HLF-LIFE ctivity: Number of disintegrations per unit time: (t) = N(t) = N 0 exp( t) = 0 exp( t) (6.3) This has the same exponential fall off with time as N(t) Time (sec) L8-1

2 BP RDIOCTIVE DECY Half-life: Time for half the radioactive nuclei in the sample to decay. Substituting N 0 = N 0 /2 and t = t 1/2 into Eq. (6.2) gives t 1/2 = ln2/ (6.4) The figure above shows the activity of a sample decaying at a rate of exp(-t). The half-life of this sample = ln2 ( 0.7 s). DECY CHINS When nuclei decay into stable nuclei B, the number of each present at time t is N (t) = N (0)e λt and N B (t) = N (0)(1 - e λt ) (6.5) where only nuclei are present initially. The number of nuclei (parent nuclei) decreases with time. The number of nuclei B (daughter nuclei) increases from zero, initially, and approaches N (0) as t, i.e. all the parent nuclei eventually become daughter nuclei. The total number of nuclei is constant: N (t) + N B (t) = N (0). If nuclei B are also radioactive, the above equations do not apply, since, as nuclei B are produced, they also decay. The daughter nuclei of B may also be radioactive and a decay chain is set up: B C etc. We shall give a number of examples of decay chains in the next section. TYPES OF RDIOCTIVE DECY The figure below shows how a variety of decay mechanisms transform an initial (parent) nucleus into different final (daughter) nuclei. Z X N Here we shall consider a number of basic decay mechanisms. They are: alpha decay; beta decay (, + and electron capture); gamma decay and internal conversion; spontaneous fission. L8-2

3 BP RDIOCTIVE DECY LPH DECY 4 2He Z X N 4 Z -2Y N -2 Emission of the alpha reduces the mass of the nucleus The parent nucleus Z X emits an particle. The daughter product is 4 mass units lighter and N 4 Z. with 2 fewer units of electric charge: -2 X N -2 Characteristics of alpha decay If it is energetically favourable for a nucleus to lose mass, the particle (charge +2e and mass u 3.7 GeV) is most commonly emitted because it is a tightly bound system. lpha decay occurs almost exclusively in heavy nuclei because B/ decreases with when is large and so the daughter product of decay is more stable than the parent. Mass numbers of nearly all emitters > 209 and typical -particle kinetic energies E = 4 to 6 MeV. lpha particle energies are well-defined. s α particles pass through matter, they lose energy rapidly. lpha particles of a few MeV are easily stopped by paper or skin e.g. the range of a 5 MeV is about 3.5 cm in air and 20 m in a silicon detector. lpha decay mechanism lpha particles are tightly bound systems that exist within the potential well created by the daughter nucleus. L8-3

4 BP RDIOCTIVE DECY The Q value must be positive for the decay to take place at all., Otherwise it is not possible for the particle to tunnel through the barrier and escape. Prior to emission, the particle is considered to be confined within the potential well. It is assumed to be pre-formed inside the nucleus (not true in general). The pre-formation factor F is difficult to calculate and, normally, it is taken to be 1. The confined alpha particle has kinetic energy and oscillates to and fro many times per second (frequency f ~10²² s -1 ). Each time it reaches the surface, there is a small but finite probability P that the particle can tunnel through the barrier and be emitted. This is a quantum-mechanical process related to the wave nature of the particle. Once it has penetrated the barrier, the particle is repelled away from the daughter nucleus and escapes. crude calculation for 238 U decay gives: P ~ 10-39, which, indeed, is very small. However, the product of f and P gives a rate of escape from the nucleus of about per second or about 1 chance in 3 billion years, which is comparable with the measured half-life of 4.5 billion years. The probability P is very dependent on the Q value. Increasing the Q value by 1 MeV decreases the half-life by a factor of about 10 million! Higher-mass, active nuclei are generally less stable, because they have higher Q values for - decay and, hence, shorter lifetimes. BET DECY Nuclei with either too many protons or too many neutrons will undergo β decay via the weak nuclear force. neutron-rich nucleus will undergo β emission. proton-rich nucleus will either emit a β + particle or be transformed by capturing an atomic electron in a process called electron capture. β emission β - _ n p Z X In β decay, the charge on the nucleus increases by one unit. The β particle is an electron (mass u Z 1 Y created at the moment of decay. second light particle, - antineutrino ( 511 kev and charge -e). It is considered to be ) - is also created and L8-4

5 BP RDIOCTIVE DECY emitted. It has no charge and very small mass, which generally is assumed to be zero. It interacts extremely weakly with matter. β decay is a three-body process - the kinetic energy released is shared between the β particle and the antineutrino. This results in emitted β particles having a distribution of energies, from 0 to the maximum allowed by the Q value (end point energy). Electron intensity End point energy Electron energy β decay involves the transformation of a neutron into a proton inside the nucleus: n p (6.6) Energy must be conserved and so the transformation given in Eq. (6.6) can occur only if the daughter nucleus is lighter (more stable) than the parent. This means that the Q value: P md ) 2 Q ( m c (6.7) must be > 0. Note that the masses m P and m D, for the parent and daughter, respectively, are atomic not nuclear masses and include the masses of the atomic electrons. beta particle is much lighter than an α particle. Its speed, therefore, for a given energy is much greater and it is much more penetrating. few mm of material will stop a 1 MeV β particle. β + emission β + Z X p n Z 1 X + decay changes a proton rich nucleus into a more stable isobar. The nuclear charge is decreased by one unit. + particle is an antielectron, called a positron. It is identical to an ordinary electron except that it is positively charged. Effectively, + decay converts (via the weak nuclear force) a proton L8-5

6 BP RDIOCTIVE DECY into a neutron and a positron. neutrino is also created in the process. Note that this is an ordinary neutrino not an antineutrino. p n (6.8) There are 3 bodies in the final state and the positrons are emitted with a continuous range of energies, as are electrons in β decay. Using energy conservation, the + decay Q value, using atomic masses, is given by P md 2m) This must be greater than zero for the process to be able to occur. 2 Q ( m c (6.9) Electron capture Electron Z X p n Z 1 X Electron capture EC is an alternative process to + decay in that a proton is converted into a neutron. The parent absorbs an atomic electron, usually from the innermost orbit. Energy conservation gives the Q value as e - p n (6.10) Note that EC mp md ) 2 Q ( c (6.11) QEC is greater than Q by 2mc 2. In electron capture, the mass of an atomic electron is converted into energy, whereas, in + decay, energy is required to create a positron. This means that EC can occur when + decay cannot. No particle is emitted in electron capture and so, except for a very small amount of recoil energy of the daughter nucleus, the energy released escapes undetected. GMM EMISSION ND INTERNL CONVERSION γ emission nucleus in an excited state (often after a decay) generally decays rapidly to the ground state by emitting rays. L8-6

7 BP RDIOCTIVE DECY Example: 22 Na + 90% 10% EC 22 Ne* Energy (kev) 1274 ray emission reduces energy of nucleus 22 Ne 0 Gamma-ray energies E typically, are in the range 0.1 to 10 MeV and can be determined very accurately with a modern detector. E is characteristic of the emitting nucleus and are widely used to identify radioactive nuclei. Gamma rays of about an MeV do not interact strongly in matter and will penetrate many cm of moderate-density material. Internal conversion This is an alternative to emission whereby an excited nucleus de-excites by ejecting an electron from an atomic orbit. Both emission and internal conversion are due to the action of the electromagnetic force. SPONTNEOUS FISSION ND NEUTRON EMISSION Spontaneous fission Z X Nucleus splits into two pieces and releases neutrons ~ / 2 ~ Z / 2 Y ~ / 2 ~ Z / 2 Y In spontaneous fission a nucleus breaks up into two roughly equal mass fragments. The process normally is restricted to heavy nuclei for which BE/ for the fragments > BE/ for the initial nucleus. Fission also can be induced by a nuclear reaction, e.g. neutron capture. Spontaneous fission occurs only in very heavy nuclei, such as 252 Cf, when the Q value is large enough to overcome the energy needed to deform the parent into two separate pieces. Fission fragments are very neutron rich. lso, several (2 to 5) neutrons are emitted during fission. These are prompt neutrons. Their energies cover a range of ~2 MeV. L8-7

8 BP RDIOCTIVE DECY Neutrons are uncharged and deposit their energy in matter via nuclear interactions. This means that their interaction probability generally is small and their range is not well defined. Neutrons of several MeV will penetrate many 10s of cm of moderately dense materials, such as concrete. Delayed neutrons Neutron-rich fission products decay by β emission. Often, they follow a chain of decays to stability. Occasionally (in 1 to 2% of cases), a daughter is formed in an excited state that can decay by neutron emission. Compared with β decay, neutron decay is very rapid and if there is a preceding β decay, the neutron emission is delayed hence, the term: delayed neutrons. Example: 87 Br 2% Delayed neutron Prompt neutrons 98% 87 Kr* 86 Kr* 87 Kr L8-8

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