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# 5.3.2 Fundamental Particles

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5.3.2 Fundamental Particles
5.3 Nuclear physics G485 Fields, Particles, Frontiers of Physics 5.3.1 The Nuclear Atom 5.3.2 Fundamental Particles 5.3.3 Radioactivity 5.3.4 Fission and Fusion Ks5 OCR Physics H158/H558 Index Mr Powell 2012

5.3 Nuclear Physics Assessable learning outcomes..
(a) describe qualitatively the alpha-particle scattering experiment and the evidence this provides for the existence, charge and small size of the nucleus. (b) describe the basic atomic structure of the atom and the relative sizes of the atom and the nucleus; (c) select and use Coulomb’s law to determine the force of repulsion, and Newton’s law of gravitation to determine the force of attraction, between two protons at nuclear separations and hence the need for a short-range, attractive force between nucleons (d) describe how the strong nuclear force between nucleons is attractive and very short-ranged; (e) estimate the density of nuclear matter; (f) define proton and nucleon number; (g) state and use the notation.... for the representation of nuclides; (h) define and use the term isotopes; (i) use nuclear decay equations to represent simple nuclear reactions; (j) state the quantities conserved in a nuclear decay.

Alpha Decay.... Alpha particles tracks

(a) describe qualitatively the alpha-particle scattering experiment and the evidence this provides for the existence, charge and small size of the nucleus.

Probing the Nucleus – Rutherford Scattering
By firing alpha particles at a heavy gold nucleus Rutherford could easily see that atoms were mostly space with a large positive nucleus in the centre.

Scattering Formulae (extension)
There are complex formulae that we can use to work out the distance of closest approach. You will not have to learn these but should appreciate some of the maths involved. At the very least the idea of the forces involved

Distance of Closest Approach (extension)

Distance of Closest Approach (extension)

Summary Question... For an alpha particle with an initial KE of 6MeV fired at a gold nucleus find the distance of closest approach of the alpha and the nucleus...

Small Nucleus.... Nucleons....

Estimate Nuclear Diameter with “Electron Diffraction”

Quick Question

(b) describe the basic atomic structure of the atom and the relative sizes of the atom and the nucleus;

(c) select and use Coulomb’s law to determine the force of repulsion, and Newton’s law of gravitation to determine the force of attraction, between two protons at nuclear separations and hence the need for a short-range, attractive force between nucleons

(d) describe how the strong nuclear force between nucleons is attractive and very short-ranged;

Where does it come from? The strong force actually acts between quarks which are found inside nucleons. It's the strong force that causes nucleons to attract. The carrier of this force is the gluon. The force ensures that the protons and neutrons in the nucleus of the atom stay together without flying apart. The nucleus of the atom is formed in this way. This force is so strong that it almost causes the protons and neutrons within the nucleus to bind to each other. This is why the minute particles that possess this force are called "gluon" meaning "glue" in Latin.

Interactions combined..
Separation/ fm Repulsive Force (N) 600 400 200 + The overall graph is a combination of electrostatic repulsion (charged quarks) and the strong force (quarks) + repulsive Typical equilibrium separation Equilibrium separation Separation/ fm attraction repulsive Force (no units) Force (no units) Separation/ fm Electric force dominates at larger separations u d strong nuclear force dominates at smaller separations 104 attraction d u

Main properties of the strong nuclear force are:
At typical nucleon separation (1.3 x 10-15m) it is a very strong attractive force (104 N). At much smaller separations between nucleons the force is very powerfully repulsive. Beyond about 1.3 x 10-15m separation, the force quickly dies off to zero. Thus, the strong nuclear force is a very short-range force. The much smaller Coulomb force between protons has a much larger range and becomes the only significant force between protons when their separation exceeds about 2.5 x 10-15m. The strong nuclear force is not connected with charge. Proton-proton, proton-neutron and neutron-neutron forces are the same. (The force between protons, however, must always be modified by the Coulomb repulsion between them.)

Fundamental Forces

M Atomic Radius.... Element A A1/3 R in fm Carbon Oxygen Silicon
12 2.29 2.75 Oxygen 16 2.52 3.02 Silicon 28 3.04 3.64 Calcium 40 3.42 4.10 Vanadium 50 3.68 4.42 Strontium 88 4.45 5.34 Indium 115 4.86 5.84 Various types of scattering experiments suggest that nuclei are roughly spherical and appear to have essentially the same density. The data are summarized in the expression called the Fermi model; r0 = 1.2 x 10-15m = 1.2fm r = atomic radius A = mass number (nucleons) Can you plot a graph and show that this formulae is correct and the constant is 1.2fm FACT The diameter of the nucleus is in the range of 1.6fm (1.6 × 10−15 m) (for a proton in light hydrogen) to about 15 fm (for the heaviest atoms, such as uranium).

P Finding R0

(e) estimate the density of nuclear matter;

Summary & Question Calculate the radius of an oxygen nucleus which has 16 nucleons.. r=r0A 1/3= 1.4 x x (16)1/3 r=3.5 x 10-15m (3.5fm)

Nuclear Density – is massive!

(f) define proton and nucleon number & (g) state and use the notation
(f) define proton and nucleon number & (g) state and use the notation.... for the representation of nuclides;

(h) define and use the term isotopes;

(i) use nuclear decay equations to represent simple nuclear reactions;

(i) use nuclear decay equations to represent simple nuclear reactions;

(j) state the quantities conserved in a nuclear decay.

5.3.1 The Nuclear Atom Covered in my lesson
Revised/ Made my own notes or reviewed at home Attempted Exam or Revision Questions (a) describe qualitatively the alpha-particle scattering experiment and the evidence this provides for the existence, charge and small size of the nucleus (b) describe the basic atomic structure of the atom and the relative sizes of the atom and the nucleus; (c) select and use Coulomb’s law to determine the force of repulsion, and Newton’s law of gravitation to determine the force of attraction, between two protons at nuclear separations and hence the need for a short-range, attractive force between nucleons (d) describe how the strong nuclear force between nucleons is attractive and very short-ranged; (e) estimate the density of nuclear matter; (f) define proton and nucleon number; (g) state and use the notation A,Z,X for the representation of nuclides; (h) define and use the term isotopes; (i) use nuclear decay equations to represent simple nuclear reactions; (j) state the quantities conserved in a nuclear decay. Next Steps for me? / (what do I need to ask for help on)

E Q2 June 07.... R = R0A(1/3) The table shows data for some nuclei.
1 eV = 1.6 ×10-19 J & speed of electromagnetic radiation = 3.0 × 108 ms-1 (a) (i) Show that these data support the rule that where R0 is a constant; R = R0A(1/3) (ii) The mass of a nucleon is about 1.7 × kg. Calculate the density of nuclear matter. (6 marks) (b) (i) Explain what is meant by the binding energy of a nucleus. (ii) Show that the total binding energy of a sodium-23 nucleus is about 3 × J. (iii) Calculate the mass-equivalent of this binding energy. (5 marks)

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