Activity: Fusion and fission

Aims

  • Understand why energy will be released when two small nuclei fuse.
  • Solve problems involving fusion.
  • Discuss the conditions required for fusion.
  • Understand why energy is released when large nuclei split into two.

Fusion

Let's consider the BE/nucleon curve again.

We can see that theoretically

H presubscript 1 presuperscript 2 space plus H presubscript 1 presuperscript 2 space rightwards arrow space H presubscript 2 presuperscript 4 e

Use the graph to calculate:

  • The BE of 2H
  • The BE of 4He
  • The difference in BE before and after the H nuclei fuse to make He.

If this reaction took place what the BE would increase, this energy would have to be released in the form of gamma radiation.

Calculate the energy released in the following reactions

H presubscript 1 presuperscript 2 plus H presubscript 1 presuperscript 2 rightwards arrow H presubscript 2 presuperscript 4 e H presubscript 1 presuperscript 2 plus H presubscript 2 presuperscript 3 e rightwards arrow H presubscript 2 presuperscript 4 e plus p presubscript 1 presuperscript 1

In these reactions the energy can be given to the KE of the two particles formed.

  • What effect does increase of KE have on the properties of a gas?
  • Why couldn't the He nucleus in the first example gain KE?

Think about conservation of momentum

  • What is the total momentum at the beginning?
  • What is the total momentum at the end?

  • the fusion reaction releases several MeV of energy, approximately how much energy is released when a molecule of coal is burnt?

Initiating fusion

To make to nuclei fuse you must make them so close that the strong force pulls them together

  • Approximately how close do they need to be?
  • If two nuclei are 10 -10m apart will they attract or repel?

To get two nuclei close enough together they need to be thrown towards each other very fast. When a gas is heated the particles move faster and so will get closer to each other when they collide. We can estimate how hot the gas would have to be for the nuclei to fuse.

When two protons approach each other KE is converted to electrical PE (kQq/r where k=9x109 Nm2C-2)

  • Calculate the KE required for the protons to become 10-15 m apart.

From our study of gases we know that average KE of gas molecules = 3/2 kT where k = Boltzmann's constant 1.38 x 10-23 JK-1

  • Calculate the temperature of gas with particles traveling with this KE.

Pretty hot eh? Actually a bit of an overestimate but you get the idea that it's not so easy to get nuclei to fuse. Not only do you need a high temperature but the gas must be high density or the nuclei will never collide. This is what it's like in the core of the sun where hydrogen nuclei fuse to form helium.

  • Why are there no electrons around the hydrogen and helium nuclei in the core of the sun?
  • Why is the density of the sun's core so high?

The same conditions can be achieved in an atomic explosion but to achieve controlled fusion is a bit of a challenge.

One minute physics on fusion

Fission

Let's now take a look at the other end of the curve.

Use the graph to estimate

  • the BE of a nucleus with 200 nucleons.
  • the BE of a nucleus with 100 nucleons
  • the energy released if a nucleus with 200 nucleons split in two.

We can see that when a large nucleus splits into two smaller nuclei the BE increases resulting in a release of about 100 MeV of energy.

  • What happens to this energy?

When a nucleus splits it rarely splits into two identical halves, here is an example:

U presubscript 92 presuperscript 236 rightwards arrow B presubscript 56 presuperscript 142 a plus K presubscript 36 presuperscript 92 r plus N cross times n presubscript 0 presuperscript 1

  • How many neutrons must have been thrown out?
  • using the data below calculate the energy released.

mass 236U = 236.045563 u
mass 142Ba = 141.916361 u
mass 92Kr = 91.926270 u
mass 1n = 1.008664 u

The energy from the fission reaction is used in nuclear power stations more about that in the section on energy production.

Fusion Power problems

fission and fusion multiple choice

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