7: Atomic and Nuclear Physics

7.3 Nuclear reactions, fission and fusion

Nuclear reactions

Einstein’s Mass-Energy Relation

Q1. When 1kg of petrol is burned, 5 x 107 Joules of energy is released. What mass would this represent ?

E = mc2E = Energy (Joules)m = Mass defect (kg)c = speed of light (3 x108 ms-2)

Atomic mass units

Nuclear masses are expressed in atomic mass units:

 

Q2. If the loss in mass during a reaction is 1u determine the energy released in Joules then convert it into electron-volts (eV).

This should show that...

One atomic mass unit (1u) is equal to 1/12th of the mass of a carbon-12 atom.

1u = 1.66 x 10-27 kg

1u = 931.5 MeV

Q3. When 1kg of Uranium-235 undergoes fission, 8 x 1013 J of energy is released. What is the decrease in mass in...

a. Kilograms b. Atomic mass units

Binding Energy

This is defined as... 

 Mass (kg) Mass (u)

Proton 1.673 x 10-27 1.00728Neutron 1.675 x 10-27 1.00867Electron 9.110 x 10-31 0.00055  

... the work done in separating a nucleus into its constituent parts.

ExampleEstimate the binding energy of the helium nucleus (mass of Helium nucleus = 4.00151 u).

i. Find the mass of the constituents of the nucleus... ii. Find the mass defect in u and convert to kg...

iii. Calculate the energy equivalent in Joules and in MeV...

iv. Often the binding energy per nucleon is more informative...

TransmutationTransmutation is the conversion of one chemical isotope into another by a nuclear reaction.Beta decay is an example of natural transmutation.

Artificial transmutation may occur if you bombard a nucleus with another particle, such as a neutron…E.g.

Q. What particle is represented by X in this example of artificial transmutation?

N + n → C + p 14 7

1 0

11

14 6

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Fission

If a heavy nucleus such as Uranium-235 absorbs an extra neutron, it becomes unstable and splits into two lighter nuclei.The total binding energy of both of these fragments is greater than that of the original uranium nucleus. The difference in energy is released. The energy is released as kinetic energy of the fission products.

n U 235

92

Ba144

56

Kr90

36

n

n

γ

Fusion

When two light nuclei such as Hydrogen or Deuterium are forced to combine forming a new, heavier nucleus, the binding energy per nucleon increases. The difference in binding energy between the reactants and the fusion products is again released.

n

H21

He 3

2

H2

1

Fusion in Stars

Production of Plutonium

In a nuclear reactor for a power station, uranium is often bombarded with neutrons to cause artificial transmutation. If the neutrons move too fast, they will not be absorbed (they pass straight through the nucleus). A moderator (e.g. graphite) is used to slow them down.

One typical reaction in the reactor produces plutonium after a chain reaction:

1. Uranium-238 absorbs a neutron and turns into U-2392. U-239 decays by Beta emission to produce Neptunium-2393. Np-239 decays by Beta emission to produce Plutonium-239 (Pu-239)Q. Write a nuclear equation for each of the changes above.   

Production of Plutonium

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