Nuclear Reactions

Topic 7.2

The Atomic Mass Unit

• 1 amu is defined as 1/12 of the mass of a carbon-12 atom
• This is an average value that includes all protons, neutrons, and electrons

• 1 u = 1.6605402 x 10-27 kg

• Mass p+ = (1.6726231 x 10-27)/(1.6605402 x 10-27) = 1.007276 u
• We can do similar calculations for masses of n0s and e-s:

• Mass n0 = 1.008665 u

• Mass e- = 0.0005386 u

Binding Energy

• The Strong Force binds protons and neutrons together in the nucleus
• In order to separate them some work must be done, or energy supplied.
• Binding energy is what is required to completely separate all the nucleons in a nucleus
• If we were to go the opposite direction and put a nucleus together from constituent parts, energy would then be released.
• The energy release is described by the equation

• This means that energy released as a result of assembling a nucleus corresponds to a loss of mass.

Mass Defect

• Since mass is lost during nuclear assembly the mass of the products of a nuclear reaction is less than the individual particles that make it up.
• Mass defect (δ) is the difference between the masses of the product nucleus and the sum of the masses of the constituent particles

• The binding energy is the energy equivalent of the mass defect.

Example

• Total mass of a Helium atom is 4.0026 u
• 

•  4.0319 u

Finding The Binding Energy

• Since BE is equivalent to mass defect we can use E = mc2 to find the energy:

• Using that formula with 1 u yields:

• Convert J to eV:

• Or

Example, Continued

• Earlier we calculated the mass defect for a helium nucleus to be 0.0304 u.
• Use the conversion factor from the previous page to determine the binding energy for the helium nucleus:

0.0304 u     931.5 MeV       =    28.3 MeV                                                                                                 1 u    

Binding Energy Curve

• Shows a plot of BE per nucleon vs. A (mass number)
•  The higher the BE the more stable the nucleus
• The maximum occurs at A = 62, which is nickel-62
• Other peaks along the curve correspond to stable nuclei
• Hydrogen would be at zero since there is only one particle in its nucleus
• The sharp initial curve is due to the fact that each time a nucleon is added to a small nucleus there is a large effect in terms of BE
• Eventually it levels out:  strong nuclear force acts at short distances, so is only felt between neighboring nucleons.  After a certain point there isn’t much difference between a nucleus of 40 particles compared to a nucleus of 140 particles.

Energy Released in Nuclear Decay

• Find the change in mass between reactants and products:
• Δm = total mass reactants – total mass products
• If Δm is positive it means energy is released in the reaction, therefore decay can occur spontaneously
• If Δm is negative it means energy must be absorbed by the reactants before the decay can occur
• Not all nuclei decay: this determines which decays are spontaneous.
• The energy released takes the form of KE, so the smaller the particle the faster it moves

Nuclear Fission

• Occurs when a large nucleus absorbs a neutron and splits into smaller nuclei along with more neutrons
• Spontaneous (naturally occurring) fission is rare
• The product neutrons can then in turn cause more fission:  a chain reaction
• A certain mass of fissionable material (critical mass) must be present to sustain the chain reaction

Nuclear Fusion

• Occurs when two smaller nuclei join together to form one larger nucleus, and often extra small particles.
• A tremendous amount of energy is released in the process.
• For a long time it was thought that fusion could not be confined in a laboratory setting due to the very high temperatures involved
• New methods are being developed in which the plasma (ionized particles) involved in fusion is constrained by magnetic field lines, so it never has to contact any surfaces.  This structure is called a tokamak.

Fission vs. Fusion

• A dividing line exists on the BE curve we saw earlier that extends downward from the maximum at A = 62
• Atoms to the left are smaller, so can become more stable by fusion
• Atoms to the right are larger, so become more stable by fission
• It is worth noting that both processes carry their own sets of benefits and risks