1. Nuclear Reactions
Fission and Fusion

2. A brief history…
1919: Ernest Rutherford experimented with bombarding nitrogen gas molecules with alpha particles emitted from bismuth-214
Discovery: faster moving particles were produced, and these could travel farther than the alpha particles!
“New” particles also deflected in a magnetic field like a positive particle

3. A brief history… Conclusion: The faster moving particles were protons
Artificial Transmutation:
The change of one element to another through the bombardment of a nucleus
More experiments to determine exact nature of the particles and how they were “created” done with a cloud chamber…

4. Cloud Chambers
Invented ~1911 by a Scottish Atmospheric Physicist (C.T.R. Wilson) to experiment with rain clouds.
Enclosed environment made to be supersaturated (originally with water vapor, now commonly ethanol)
Ions introduced to this environment would attract water molecules (which are polar), forming clouds…
Earned a share in the
1927 Nobel Prize in
Physics for the invention…

5. Cloud Chambers Why would this be useful for Rutherford? Video
Water vapor condenses around ions
An alpha particle is ionizing radiation, thus leave a LOT of ions in its path
Water vapor would condense around these ions, leaving a vapor trail showing where an alpha particle had been…
Video

6. Rutherford’s Theories…
If proton was simply “chipped off” the Nitrogen nucleus by the alpha particle, there should be 4 visible tracks in the cloud chamber:
The original alpha particle BEFORE collision
The alpha particle AFTER the collision
The “chipped off” proton
The Nitrogen nucleus, now charged, as it recoiled after the collision

7. Rutherford’s Theories…
If alpha particle was absorbed, and that caused the proton to be pushed out, then there should be 3 visible tracks:
The alpha particle before collision
The proton emitted after the collision
The path of the recoiling nucleus (now Oxygen)
This theory (artificial transmutation) was supported in 1925

8. Balancing Nuclear Equations:
Note: Deuteron = Hydrogen-2 atom, a.k.a Deuterium
Example problem:
A sample of Oxygen-16 is bombarded with neutrons. If one of the resulting products is a deuteron, what is the resulting nucleus?

9. Unified Mass Unit (u)
A unit adopted by scientists that is more appropriate for masses along the order of magnitude of atomic masses
1 u = 1.66 x kg
Mass of an electron (me) = u
Mass of a proton (mp) = u
Mass of a neutron (mn) = u
Mass of 1 H atom (mH) = u

10. Mass-energy equivalence
Einstein hypothesized a relationship between mass and energy in 1905
Many years later, data from nuclear reactions showed that his hypothesis was indeed true
c = 3.00 x 108 m·s-1
m = mass (kg)
E = Energy (J)

11. Mass-energy equivalence
Used to calculate the Rest Energy of a mass
Used to calculate the amount of energy released in nuclear reactions
For Example:
Calculate the amount of energy released when 1.00 kg of fuel is used up in a nuclear reactor…

12. Binding Energy
All atomic nuclei have a total mass that is lower than the sum of the masses of each individual particle
For example: The EXPECTED mass of an atom of Helium would be the sum of the mass of 2 neutrons, 2 protons, and 2 electrons:
2( u) + 2( u) + 2( u) = u
The MEASURED mass of an atom of helium has been found to be u
a difference of u
This difference is known as the Mass Defect of the atom

13. Binding Energy
…a measure of the energy needed to keep a nucleus together
Binding Energy is the energy equivalent of the mass defect
E = mc2
E = (1.66 x kg)(3.00 x 108 m·s-1)2
E = 1.49 x J = 931 MeV
(Since 1 eV = 1.6 x J)

14. Binding Energy Example:
Calculate the binding energy of Oxygen-16. The measured mass of Oxygen-16 is u
8 electrons+8 protons+8 neutrons
8me + 8mp + 8mn = mexpected
= 8( u) + 8( u) + 8( u)
= u u u
= u

15. Binding Energy Example:
Calculate the binding energy of Oxygen-16. The measured mass of Oxygen-16 is u
mdefect = mexpected – mmeasured
= u – u
= u
Eb = mdefect · (931 MeV·u-1)
Eb = ( )(931)
= 128 MeV

16. Binding Energy Curve

17. Nuclear Reactions
Fission: A reaction that involves the splitting of a large, unstable nucleus into 2 or more smaller, more stable nuclei

18. Nuclear Reactions
Fusion: A reaction that joins two very light nuclei to form a heavier nucleus
Picture source:

19. Nuclear Reactions and Binding Energy
Nuclei with higher amounts of binding energy per nucleon are more stable than those with lower amounts of binding energy per nucleon.
Fission and fusion processes each release large amounts of energy as the nuclei join or split to form more stable products.
To predict how much energy can result from a nuclear reaction, we use a binding energy curve…

20. Binding Energy Curve

21. Nuclear Fission
Only takes place in certain very heavy elements, such as Uranium-235
Fissile Uranium-235 is used in nuclear reactions:
Nucleus bombarded with a neutron to begin a chain reaction…

22. Binding Energy Curve
Example: Use the binding energy curve to predict the amount of energy released when Uranium-235 undergoes fission to produce two Palladium-117 fragments.
Eb for 235U = 7.6 MeV/nucleon
Eb for 117Pd = 8.4 MeV/nucleon
The difference between these values, multiplied by the total number of nucleons, is equal to the amount of energy released in the reaction:
(0.8 MeV/nucleon) x (235 Nucleons) = 188 MeV

23. What is the energy equivalent of 1 u?
319 MeV
931 eV
319 keV
931 MeV D

24. The unified mass unit is defined as
the mass of one neutral atom of Carbon-12
1/12 of the mass of one neutral atom of Carbon-12
1/6 of the mass of one neutral atom of Carbon-12
The mass of the nucleus of Carbon-12 B

25. How many Joules of energy is 128 MeV?
8.00 x 1020 J
8.00 x 1026 J
2.05 x J
2.05 x J
1 eV = 1.6 E -19 J
128 e 6 eV = 2.05 E -11

26. Which nucleus is most likely to be part of a fission reaction?
Carbon-14
Deuterium
Plutonium
Potassium-40 C

27. Fission Reactions
Self-sustaining (chain) reactions: when enough neutrons are produced to naturally enable the reaction to continue until all fissile material is gone
Examples: Nuclear Reactors in Power Plants; Bombs dropped on Hiroshima and Nagasaki in WWII
Critical Mass: The amount of fissile material required to sustain a fission reaction

28. Nuclear Fusion Reactions
Conditions required for fusion reactions:
Very high temperatures (because nuclei need very high kinetic energies)
Very densely packed (to ensure that enough collisions will occur), therefore:
Very high pressures
Problems with creating fusion on Earth:
Containment is a huge problem
At temps required, atoms would ionize and technically would become a plasma

29. Nuclear Fusion Reactions
Proton-Proton Cycle = the fusion reaction that is the source of energy in young/cool stars such as the sun:
The first two reactions in the cycle must occur twice
Total energy released = 24.7 MeV

30. Fusion Example
Calculate the energy released when a proton and a deuteron undergo fusion to produce helium-3.

31.                                                                                                                                                                                                                                                 
Figure from Physics for Scientists and Engineers (6th ed.) by Serway and Jewett (Thomson Brooks/Cole, 2004).