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Nuclear Radius

Nuclear Radius. Nuclear Physics Lesson 11. Homework . Research and explain how electron diffraction can be used to determine the radius of the nucleus (6 Marks) Past Paper Question on today’s material. Complete both by Next Lesson. Learning Objectives.

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Nuclear Radius

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  1. Nuclear Radius Nuclear Physics Lesson 11

  2. Homework • Research and explain how electron diffraction can be used to determine the radius of the nucleus (6 Marks) • Past Paper Question on today’s material. • Complete both by Next Lesson.

  3. Learning Objectives • Know how to determine a value for the index for an equation of the form y = kxn.  EMPA! • State and use the equation for dependence of radius on nucleon number. • Calculate nuclear density. • Recall the implications of the high nuclear density compared to atomic density.

  4. Nuclear Radius The nuclear radius, R, can be shown to be related to the nucleon number, A according to:- Where r0 and n are constants. Given R for a number of nuclei with a variety of A, how can we determine r0 and x?

  5. Data

  6. Data (Suggestion)

  7. Finding r0 and x This is in the form y = mx + c. Logging both sides • log (AB) = log A + log B • log (An) = n log A

  8. Finding r0 and x Plotting ln R against ln A should give a straight line with gradient = n and intercept = ln r0 Note that elnr0=r0.

  9. Excel Plot From graph:- gradient n = 1/3 intercept = ln r0 intercept = -34.49 r0 = 1.05 fm

  10. Equation • Dependence of radius on nucleon number:- [The term A1/3 means the cube root of A, the nucleon number.  The term r0 is a constant with the value 1.4 × 10-15 m.  R is the nuclear radius.] What physical quantity is r0? Rearrange in the form of A=. Try working out R for Gold (A =197 ) and Carbon (A=12)

  11. Nuclear Density • Radius of a carbon nucleus ~ 3.2 × 10-15m. • Radius of a gold nucleus ~ 8.1 × 10-15m. • Mass of a carbon nucleus ~ 2.00 × 10-26kg. • Mass of a gold nucleus ~ 3.27 × 10-25kg. • What are the densities of the nuclei?

  12. Nuclear Density Recall that density is given by:- You can assume that the nucleus is spherical so that V = 4/3 πR3, so the density is given by:-

  13. Nuclear Density • Density of carbon nucleus ~ 1.46 × 1017 kg m-3. • Density of gold nucleus ~ 1.47 × 1017 kg m-3. • Very high! One teaspoon = 500 million tonnes. • So pretty much the same, regardless of element. • Ext: Work out mass of neutron star based on this density. How does it compare to solar mass?

  14. Why the same? Where u is the atomic mass unit (1/12th mass of carbon atom, close to mass of proton) So:- Density does not depend on A!

  15. Nuclear Density • Nuclear density >> Atomic Density • This implies:- • Most of an atom’s mass is in its nucleus. • The nucleus is small compared to the atom. • An atom must contain a lot of empty space.

  16. Example Exam Questions • Q1: • (a)If a carbon nucleus containing 12 nucleons has a radius of 3.2 × 10-15m, what is r0? • (b) Calculate the radius of a radium nucleus containing 226 nucleons. • (c) Calculate the density of a radium nucleus if its mass is 3.75 × 10-25 kg. • Q2: A sample of pure gold has a density of 19300 kg m-3. If the density of the gold nucleus is 1.47 × 1017kg m-3 discuss what this implies about the structure of a gold atom.

  17. Stretch & Challenge An often quoted random fact is that a sugar cube of a neutron star has mass roughly equal to the mass of all the humans on Earth. Making some reasonable approximations, show whether or not this is true.

  18. Clues Diameter of a neutron star ~ 25 km. Mass of a neutron star ~ 4 ×1030 kg Total number of humans on Earth ~ 6 billion Average mass of humans ~ 70 kg.

  19. Stretch & Challenge Assume 6 billion humans of mass 70 kg:- Mass of human population = 6 × 109 × 70 kg = 4.20 × 1011 kg. Density of neutron star = 4×1030kg/(4/3π(12,500)3) = 4.89 × 1017 kg m-3 Mass of neutron star = density × volume = 4.89 × 1017 kg m-3 × 10-6 m3 = 4.89 × 1011 kg

  20. Learning Objectives • Know how to determine a value for the index for an equation of the form y = kxn.  EMPA! • State and use the equation for dependence of radius on nucleon number. • Calculate nuclear density. • Recall the implications of the high nuclear density compared to atomic density.

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