5 nuclear stability and radioactive decay
- 1. Nuclear Stability and Radioactive Decay 1
- 2. Nuclear stability When a graph of neutron number (N) against proton number (Z) graph is plotted for all known nuclides – fig 1 is obtained. 2
- 3. 3 Stable nuclides of lighter elements have ratio N/Z ≈ 1 As Z increases, stability line curves upwards. Heavier nuclides need more and more neutrons to be stable. (N/Z ratio ≈ 1.5) There is an upper limit to the size of a stable nucleus, because all nuclides with Z higher than 83 are unstable. Most of the atoms in the world have stable nuclei, but all nuclei except hydrogen contain at least 2 protons Positively charged protons repel each other, Coulomb’s law shows that 2 protons 2 x 10-15 m apart produce a repulsive force of about 50 N. (electric repulsive force) So why does the nucleus not blow apart?
- 4. 4 Another force acts between nucleons – strong nuclear force. (100 times stronger than the electric repulsive force). Strong nuclear force is attractive over short distances (0.5 x 10-15 m) and so holds the nucleons together. In stable nuclei these forces hold the nucleons together as they are balanced, imbalance makes nuclei unstable. Atoms of radioactive materials have unstable nuclei and decay to become more stable by emitting radiation in one or more of the following ways: 1. Alpha decay (α) 2. Beta minus decay (β-) 3. Beta plus (positron) emission (β+) 4. Electron capture 5. Isometric transition or gamma decay (γ)
- 5. 5 A nuclide may undergo several decays before it becomes stable – called a decay chain. Parent nuclide – the nuclide at the beginning of a particular decay chain. Daughter nuclide – new nuclide produced by decay (may or may not be stable). Alpha decay An alpha-particle is a helium nucleus and is written as 4 2α or 4 2He – consists of 2 protons and 2 neutrons. This decay can be represented by a nuclear equation: A ZX → A-4 Z-2X + 4 2α Notice that the top and bottom numbers balance on each side of the equation. Often followed by gamma ray and sometimes a characteristic X-ray emission.
- 6. 6 An α particle is emitted in the decay of many elements with a proton number greater than lead (Z › 82) Polonium-208 emits an alpha particle and becomes an isotope of lead: 208 84Po → 204 82Pb + 4 2α Every decay releases 5.1 MeV of energy – KE of the ejected α-particle (majority) and recoil of the daughter nuclide Nearly all α-emitters eject most of their alpha particles with a single energy value (energy value is characteristic of the nuclide)
- 7. Beta decay 7 Emitted by nuclides with an excess of neutrons over protons. This is the emission of an electron from the nucleus – but there are no electrons in the nucleus! One of the neutrons changes into a proton (remains in nucleus) and an electron (emitted as β- particle) So proton number (Z) increases by one, but nucleon number (A) remains the same and is represented by the nuclear equation: A ZX → A Z+1X + 0 -1β Platinum-199 changes to gold-199 by β-decay 199 78Pt → 199 79Au + 0 -1β
- 8. 8 Each decay of a Pt-199 nucleus releases 1.8 MeV of energy – might expect it to appear as KE of β-particles. This does not happen as emitted β-particles have a range of KEs – see graph on the board. Wolfgang Pauli (1930) suggested another particle is also emitted during the decay (antineutrino) – KE shared between electron and the antineutrino. (discovered 1956) The antineutrino (antimatter particle) has no charge and no mass – decay equation then becomes: 199 78Pt → 199 79Au + 0 -1β + 0 0ν¯ All β-emitters produce β-particles with a range of energies up to a maximum value – this value is characteristic of the nuclide.
- 9. Gamma-emission 9 Gamma-emission results in no change in the structure of the nucleus, but makes the nucleus more stable – reduces energy of the nucleus. A nucleus that emits an α-particle or β- particle often left in an excited state – losing surplus energy by emitting a γ-ray photon. Aluminium-29 changes to silicon-29 by β-emission, and then a γ-photon of energy 1.4 MeV 29 13Al 29 14Si 29 14Si β¯ γ 2.5 MeV 1.4 MeV Energy, hence wavelength of the γ-ray emitted is characteristic of that nuclide
- 10. Beta+ decay 10 A radio-nuclide above the stability line (see fig 1 slide 2) decays by β-emission (slide 7) – moves diagonally towards the stability band. Radio-nuclides below the stability line undergo positron- decay (β+ decay) to move diagonally towards stability band) Positron is the antiparticle of the electron – same mass but opposite charge, represented as 0 +1β or 0 +1e A proton in the unstable nucleus changes into a neutron and a positron – neutron remains, positron is ejected. General equation is: A ZX → A Z-1X + 0 +1β + ν
- 11. 11 A second particle, the neutrino v, is emitted with the positron – it is a massless, chargless particle. Notice, as always, top and bottom numbers balance. Positrons emitted by unstable nuclei which have a deficit of neutrons compared to protons Compare the following two decays: 14 6C → 14 7N + 0 -1β + 0 0ν¯ 15 8O → 14 7N + 0 +1β + ν Electron Capture In this type of nuclear change, a proton combines with an electron from an inner shell – usually the n = 1 shell Results in the production of a neutron – has the same effect on the nucleus as β+ decay (reducing Z by 1) as electron combines with a proton.
- 12. 12 Subsequently an electron will move from an outer shell to fill the space left by captured electron. Results in a characteristic X-ray photon being emitted. An example is the decay of Cr-51 to V-51 with a neutrino. 51 24Cr + 0 -1e → 51 23V + 0 0v + X-ray Energy is carried away by the neutrino and the X-ray photon. Decay chains A radio-nuclide often produces an unstable daughter nuclide – this will also decay and process continues until a stable nuclide is produced. Called a decay chain (or decay series) – the uranium-238 decay chain is shown on the next slide.
- 13. 13 238 92U 234 90Th + 4 2α 234 91Pa + 0 -1β 234 92U + 0 -1β230 90Th + 4 2α226 88Ra + 4 2α 222 86Rn + 4 2α 218 84Po + 4 2α 214 82Pb + 4 2α 214 83Bi + 0 -1β214 84Po + 0 -1β 210 82Pb + 4 2α 210 83Bi + 0 -1β 210 84Po + 0 -1β 206 82Pb + 4 2α Lead-206 is a stable isotope
- 14. Questions 1. Z number for Pb =82, F = 9 and Fe = 26. Write nuclear equations for the following decays: (a)Beta-emission from oxygen-19 (19 8O) (b)Alpha-emission from polonium-212 (212 84Po) (c)Positron-emission from cobalt-56 (56 27Co) 14