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A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Nuclear physics Syllabus Daniel Hilton 1 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Nuclear Physics – overview diagram Daniel Hilton 2 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 3 You Tube links The Discovery of the Atomic Nucleus - Dr. Brian Cox 3:28 Gold foil experiment and transmutation of Nitrogen in to Oxygen 8:15 Rutherford Gold Foil Experiment - lab 4:06 Daniel Hilton A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford experiment The Rutherford experiment or Gold foil experiment or the Geiger–Marsden experiment was an experiment to probe the structure of the atom performed by Hans Geiger and Ernest Marsden in 1909, under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester. The unexpected results of the experiment demonstrated for the first time the existence of the atomic nucleus, leading to the downfall of the plum pudding model of the atom, and the development of the Rutherford (or planetary) model. Daniel Hilton 4 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering Alpha particles from a radioactive source strike a thin gold foil. If the gold foil was 1 micrometer thick, then using the diameter of a gold atom from the periodic table, the foil is ~ 2800 atoms thick. Alpha particles produce a tiny, but visible flash of light when they strike a fluorescent screen. Daniel Hilton 5 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering Surprisingly, alpha particles were found at large deflection angles and some were even found to be back-scattered. This showed that the positive matter in atoms was concentrated in an incredibly small volume and gave birth to the idea of the nuclear atom. In so doing, it represented one of the great turning points in our understanding of nature. Daniel Hilton 6 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering Daniel Hilton 7 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive center, carrying a charge. —Ernest Rutherford Daniel Hilton 8 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Alpha scattering - “plum pudding model” Daniel Hilton 9 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Alpha scattering - “Rutherford model” Daniel Hilton 10 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 11 Rutherford Scattering – Coulomb's Law The scattering process can be treated in terms of the electrostatic force (Coulomb force) between the alpha particle and the nucleus, which is considered to be a point charge Ze. r : distance between charges; ε0 : “permittivity of free space Work done (or PE) =F r=( Daniel Hilton k qQ k qQ )r= 2 r r A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering – scattering process The scattering of the alpha particle by the central repulsive Coulomb force results in a hyperbolic trajectory. From the scattering angle and momentum, the impact parameter and closest approach to the target nucleus can be calculated. Daniel Hilton 12 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering – [Eqn is not A level] For a detector at a specific angle with respect to the incident beam, the number of particles per unit area striking the detector is given by the Rutherford formula: Daniel Hilton 13 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford scattering – playing with data We can explore Rutherfords scattering equation: 2 2 4 Ni n L Z k e N (θ)= 2 2 4 4 r KE sin (θ/2) For a fixed radiation source and target material we could place the following into one value eg Const N i n L Z 2 k 4 e2 Const = 2 2 4 r KE Thus: Const N (θ)= 4 sin (θ/ 2) We can use a spreadsheet to look at this curve. Daniel Hilton 14 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford scattering – playing with data 1 For a spreadsheet plot let Const = 1, thus N (θ)= 4 sin (θ/ 2) Daniel Hilton 15 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 16 Rutherford scattering – playing with data 1 For a spreadsheet plot let Const = 1, thus N (θ)= 4 sin (θ/ 2) Sin (θ/2) ^4 Sin (θ/2) ^4 800000.00 1000000.00 700000.00 100000.00 600000.00 10000.00 500000.00 1000.00 400000.00 300000.00 100.00 200000.00 10.00 100000.00 0.00 1.00 0 20 40 Daniel Hilton 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 17 Nuclear radius Rutherford used the conservation of energy to estimate the nuclear radius. The Alpha particle KE “becomes” electrostatic PE at it's closest approach to the nucleus, just before the Alpha particle rebounds back. Daniel Hilton A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Nuclear radius – conservation of energy Electrostatic energy of the Alpha/nucleus pair can be seen as resulting from the work done to move the two charges together from “infinity” to r [for more details see “Fields”] Work done (or PE) =F r = ( k q alpha q nucleus r2 k qalpha qnucleus )r = r Using conservation of energy we can “find”: KE before + PE before =KE after +PE after qalpha q nucleus 1/2 m v +0=0+k d q alpha q nucleus q alpha q nucleus 2 1/2 m v =k = d 4 π ϵo d 2 Daniel Hilton 18 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Nuclear radius – point of closest approach Using conservation of energy we can also “find” the distance of closest approach (ie r = d): KE before +PE before =KE after +PE after qalpha q nucleus 1/ 2 m v +0=0+k d k qalpha qnucleus k (2 e)(Ze) 2 k Z e 2 d= = = KE before KE alpha KE alpha 2 Show that for an Alumiminium nucleus (Z=13) and an Alpha particle of energy 8x10^-13J that d is ~ 7x10^-15m Daniel Hilton 19 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Nuclear radius issues Some points: 20 2 2k Z e d= KE particle The nucleus was treated as a point charge - at this level it is not. Alpha particles stop some distance away from the nucleus. It takes higher energy alpha particles to penetrate the nucleus. The values for the nuclear radius given by other particles such as protons, neutrons and electrons are slightly different. Nuclear units 1 electron volt = 1eV = 1.6 x 10^-19 joules 1 MeV = 106 eV; 1 GeV = 109 eV; 1 TeV = 1012 eV Atomic sizes are on the order of 0.1 nm = 1 Angstrom = 10^-10 m Nuclear sizes are ~ femtometers (fermis) 1 fm = 10^-15m Daniel Hilton A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 21 Nuclear radius – estimates from scattering Various types of scattering experiments suggest that nuclei are roughly spherical (but not hard spheres) and have essentially the same density. The scattering data can be summarized in an expression for the nuclear radius (called the Fermi model): R=r 0 A1/3 R : nuclear radius A: mass number r 0=(1.2±0.2) x 10−15 m=1.2 fm Daniel Hilton A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 22 Nuclear density Nuclear density is the density of the nucleus of an atom, and is used when describing objects like neutron stars. Nuclear Density = Nuclear mass / Nuclear Volume Mn ρn = Vn Let M n= A u (u=atomic mass unit =1.66 x 10−27 kg ) 3 1/3 Let V n=4/ 3π R n (nuclear radius R n=r 0 A ) Mn Au Au u ρn = = = = 3 1/3 3 V n 4 /3 π R n 4 /3 π(r o A ) 4/3 π r 3o 3u ρn = 3 4 π ro Daniel Hilton A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Nuclear density 3u ρn = 3 4 π ro This expression indicates that the nuclear density is independent of A and that the average distance between nucleons is similar, despite the element −15 Let r 0=1.05 x 10 m=1.05 fm −27 u=atomic mass unit =1.66 x 10 kg −27 3 u 3(1.66 x 10 kg ) ρn = = 3 −15 3 4 π r o 4 π(1.05 x 10 m) 17 −3 ρn =3.4 x 10 kg m Daniel Hilton 23 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density 24 Rutherford Scattering – some historical notes 1899+: Discovered the concept of radioactive half-life; proved that radioactivity involved the transmutation of one chemical element to another; differentiated and named alpha and beta radiation. Awarded Nobel Prize in Chemistry in 1908. 1909-13: Experiments on alpha scattering by nucleus, leading to... 1911: Discovery of the nucleus, theorized as a +ve charge concentrated in a very small space [Rutherford atomic model] 1917: First "splitting of the atom" - nuclear reaction between nitrogen and alpha particles, discovered (and named) the proton. 1920: Conceptualized the possible existence of the neutron - he considered that the disparity found between atomic number (Z) and atomic mass (A) due to existence of a neutrally charged particle within the atomic nucleus. He considered the neutron to be a neutral double of an electron orbiting a proton. By early 1930's it was found that the neutron was is a single particle. 1937: After his death he was interred near Isaac Newton's and J.J. Thomson in Westminster Abbey. Daniel Hilton A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Rutherford Scattering Daniel Hilton 25 A2 Physics: Unit5 - Nuclear physics - Scattering, radius and density Afterword : the alpha particle A 'diagram' of the helium-4 atom the protons (red) and neutrons show as separate particles. In an actual helium atom, the protons are superimposed in space and most likely found at the very center of the nucleus, and the same is true of the two neutrons. All four particles are most likely found in exactly the same space. Classical images of separate particles thus fail to model known charge distributions in very small nuclei [Quantum Mechanics!] Daniel Hilton 26