 NE 105 - Introduction to Nuclear Engineering Spring 2011 Classroom Session 4 - Fundamental Concepts End Nuclear Energetics Intro Classic and Relativistic.

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NE 105 - Introduction to Nuclear Engineering Spring 2011 Classroom Session 4 - Fundamental Concepts End Nuclear Energetics Intro Classic and Relativistic Calculations Photon Interactions with Matter Nuclear Energetics

2 Electron Volt Work done by one electron accelerated through a potential difference of one volt 1 eV = 1.60217646x10 -19 J Example: What is the speed (m/s) of a 12 eV 134 Xe ion? (from the chart of the nuclides: 134 Xe Weights = 133.905394 AMU) Use classic concept of KE for now amu in table 1.5 Joule = Energy, Work = Force (N) x d =kg m 2 /s 2

3 Correction of the book… REMEMBER! Please ignore the c 2. It is confusing Book: Page 6

4 4156.4 m/s ~9,300 m.p.h i.e. even very low energy ions are moving pretty fast Please remember this is ONLY for classical calculations. At energies close to c, need to use relativistic calculations

5 What is the speed of a 100.00 MeV proton: 1. 102,540 m/s 2. 5,467 g/s 3. 1.38e8 m/s 4. 13840 m/s 5. 3e8 m/s

100MeV proton = 0.46 c :close to the speed of light. i.e. classic equations do NOT hold i.e. 0.46 is likely wrong 6 What is the speed of a 100.00 MeV proton:

7 Newton Laws For over 200 years, Newtons laws worked Accurately described many physical behaviors Unifying the earth and the skies Previously: Sub-lunar sphere: impure and imperfect Skies: perfect and immutable (circle, ether)

8 Special Theory of Relativity - Effects Mass Increase with increasing velocity Increase quantified by Lorentz factor ( ):

9 Length and time are also modified relative to an objects speed For example: To find speed… Special Theory of Relativity - Effects

10 What is the kinetic energy of a 100.00 MeV proton? Hint: Relativistic speeds, i.e. use this equation: Special Theory of Relativity - Effects

The error grows as v c 11

12 Remember Relativistic calculation required when: kinetic energy ~ rest energy What is the rest mass of an electron? What is the rest mass of a p + or n 0 ? What is the rest mass of heavy ions? (Table 1.5 book) Use:eVkeVMeV

13 What is the kinetic energy of a 1 MeV electron? Rest mass of the electron, m e =0.511MeV 1. 0.511 MeV 2. 0.489 MeV 3. 0.999 MeV 4. 1 MeV 5. 0 MeV

What is the speed of a 1 MeV electron? Rest mass of the electron, m e =0.511MeV 14 1. 0.58c 2. 0.81c 3. 0.86c 4. 0.94c 5. 0.993c

Solution: 15

16 Special Theory of Relativity - Effects In Nuclear Engineering we rarely work with neutrons of more than 10MeV. We stick to classic calculations for KE of p, n,, ions, and fission fragments Homework 2.3. What is the error in computing speed of a 10 MeV neutron classically instead of relativistically?

17 What is the kinetic energy of a neutron whose relativistic mass is 10% greater than its rest mass? 1. 0.12 c 2. 0.22 c 3. 0.32 c 4. 0.42 c 5. 0.52 c

19 Photon Interactions Energy High Intermediate Low Pair Production Compton Scattering Photoelectric Effect

20 Pair Production

21 Compton Scattering

22 The Photoelectric Effect

23 Compton Scattering – The Experiment E E In 1922, Compton obtained this data Scattered X-Rays had an increase in wavelength Can you explain why?

24 Compton Scattering – Light has p! If light is a wave, then radiation scattered by an electron should have no change in wavelength In 1922, Compton demonstrated that that x-rays scattered from electrons had a decrease in wavelength. This is only possible if light is treated as a particle with linear momentum equal to p=h/ Why the equation written for the photon angle? E E

25 Follow equations But pay attention to units For wavelength please use nm

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