20. Nuclear Physics

Nuclear Physics Rutherford Alpha (He2+) Scattering Experiment Key features of the Setup:  An Alpha source  Thin Metal Foil  Gold foil  Fluorescence detector  ZnS Screen  Vacuum Chamber o Prevent collision with air Results:  Most He2+ have little or no deviation o Volume of the atom is made up mainly of empty spaces  A small fraction of He2+ were deflected by more than 90° and a very small proportion were deflected by 180° o Nucleus consists of a positive charge concentrated in a very small space Nuclide – a particular species of a nucleus that is specified by its proton and neutron number Nuclide notation: A Z X Where X is the symbol of the element, Z is the proton number, A is the nucleon number (sum of the number of protons and neutrons) Subatomic Particles Sub-atomic particle Rest mass Charge Proton ( H1 1 or p1 1 ) 1.6726 x 10-27 kg +1.6 x 10-19 C Neutron ( n1 0 ) Approximately mass of proton 1.6749 x 10-27 kg 0 Electron ( e0 1 ) 9.11 x 10-31 kg ( ≈ 1/1800 x mass of protons) -1.6 x 10-19 C Isotopes – are nuclides having the same atomic number (same element) but different mass number Atomic mass unit (u) – a unit of mass. 1u is defined as 1/12 the mass of a carbon-12 atom, 1u = 1.661 x 10-27 kg Electronvolt (eV) – is a non-SI unit for energy equal to the energy gained by an electron when it is accelerated through a potential difference of one volt. (1eV = 1.60 x 10-19 J) Gold Foil

Mass Defect  Mass of an atom is less than the sum of masses of their separate constituents – protons, neutrons and electrons  The difference between the mass of a nucleus and the mass of its constituent particles taken separately is known as mass defect o Mass defect = Mass of protons and neutrons – Nuclear mass o Z Mp + (A – Z)Mn – M  where Z: proton number; A: mass number; Mp: mass of a proton; Mn mass of a neutron; M: mass of the nucleus Nuclear Binding Energy  Binding energy is the work that would have to be done (energy absorbed) to separate a nucleus into its constituent protons and neutrons. OR  Binding energy is the energy released if a nucleus is formed from its constituent separate protons and neutrons Mass-Energy Equivalence  Einstein proposed that mass and energy are equivalent, that is, it is possible to interchange mass and energy, 2E mc .  Binding energy is the energy equivalent of the mass defect of the nucleus, 2E mc , m is the mass defect Nuclear Processes  A nuclear reaction (or process) can be represented as, o 13 7 12 6 NHC  1 1  In a nuclear process, the following are conserved o Nucleon number o Proton number o Mass-Energy o Momentum  Note: Nuclear reaction/process outlined is only one of the many possible reactions. It is unlike chemical reactions that are definite without other product. In a nuclear reactions, many different products are possible even if the initial products are the same  Calculate energy released in a nuclear process, o E = (total mass of product – total mass of reactant)c2 Binding Energy per Nucleon  Binding Energy of a nucleusBinding Energy per nucleon = Number of nucleons  It is the average energy per nucleon needed to separate nucleus into separate nucleons  It is a measure of nucleus stability. Greater binding energy per nucleon means a more stable, more tightly bound nucleus

Binding Energy per Nucleon Curve Features of the curve  The curve is experimentally obtained. There is only one such curve.  Fe-56 has the highest binding energy per nucleon at ~8.8 to 9 MeV o There exist a maximum due to two competing factors  When nucleon number is low, binding energy is low  When nucleon number is high, it means high number of protons and neutron in a tight confined nucleus  Heavy nucleus can get stability from nuclear fission (splitting) to form lighter nuclei with higher binding energy per nucleons  Lighter nucleus can get stability from nuclear fusion (combining) to form heavier nuclei with higher binding energy per nucleons o In both nuclear fission and fusion, there will be a release of energy equal to the difference in the binding energy of the products and reactants Nuclear Fission  Heavy nucleus splits into lighter nuclei of approximately equal mass  Along with emissions of neutrons  Total mass of daughter nuclei is lesser than the original nucleus (decrease in total mass), with the release of energy (in the form of KE of the daughter nuclei and/or electromagnetic energy – gamma-ray photon(s)) Mechanism of Fission 1. Neutron Capture. o A slow moving neutron is captured by the heavy nucleus  “Slow” as fission is NOT using a high energy neutron to smash up the heavy nucleus

2. Instability  The addition of the neutron in the nucleus causes the nucleus to be unstable 3. Fission  Due to the instability, the heavy nucleus is split into two or more lighter nuclei  Release of more fast moving neutrons 4. Fission Chain Reaction  Neutrons generated can cause further initiation of fission reactions when they are captured by more heavy nucleus, and so on Nuclear Fusion  Two or more nuclei of low mass number collide and combine to form heavier nucleus  Often with emission of another lighter particle  Decrease in total mass and release of energy  Initial input of energy is required. Nuclei are positively charged. Hence energy is required to overcome the electric potential energy due to the repulsive force between the two charges, so that the nuclei can come close together to react Radioactivity (radioactive decay) – is the spontaneous and random disintegration (or decay) of an unstable nucleus into a more stable one with the emission of either an alpha-particle, or a beta-particle, and/or usually accompanied by the emission of a gamma ray photon.  Spontaneous: Decay cannot be controlled and unaffected by external physical conditions (unlike a fission that requires neutron capture)  Random: Impossible to predict exactly which nucleus or when a particular nucleus will decay  Alpha Decay  Alpha-particle emitted  Beta Decay  Beta-particle emitted  In both Alpha and Beta Decays, gamma ray photons may or may not be emitted  If daughter nucleus is still unstable, further different decay can happen. This is known as decay chain Types of Radiations Radiation Nature Charge Mass Speed Energy Alpha particle (α) Helium-4 nucleus (2p + 2n), He4 2 +2e ~ 4 mproton 0.1c 3 - 7 MeV Beta particle (β) High speed electron , e0 1 -e ~ (1/1800) mproton Wide range: 0 - 0.9c 0 - 1 Mev Gamma ray photon (γ) Electromagnetic radiation of very short wavelength No charge massless c 0.1-10 MeV

Penetrating Ability vs Ionising Ability Radiation Penetrating ability: Stopped by Ionising ability Effect of magnetic and electric fields Alpha particle (α) He2+ - 2-4 cm of air - A thin sheet of paper - A thin sheet of mica - Human skin A great deal Deflect in same direction as positive charge Beta particle (β) e- - 6 cm - 3 m of air - Few mm of light metals such as aluminium (> 5 mm thick aluminium) Some Strong deflection in opposite direction to  particle Gamma ray photon (γ) - 400-500 m of air - Several cm of dense metals such as lead (a 2.5 cm thick lead absorbs about half the incident Ƴ-ray photons) - Several metres of lighter materials such as concrete Very little No effect α, β and γ in Fields α-Decay  α-particles are helium-4 nuclei (42He)  QHeYX A Z A Z 4 2 )4( )2(     Most energy Q is carried away by the α-particle o Prove by conservation of momentum and take ratio of respective kinetic energy

β-Decay  β-particle is a high speed electrons emitted from the nucleus. (NOT an orbital electron)  β-particle is produced when a neutron decays into a proton, Q 0 1- 1 1 1 0  epn  QeYX A Z A Z 0 1-)1(    β-particles detected