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The diagram shows part of an experimental fusion reactor - Scottish Highers Physics - Question 8 - 2016

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The diagram shows part of an experimental fusion reactor. The following statement represents a reaction that takes place inside the reactor. $$\text{ }^2H + \text{... show full transcript

Worked Solution & Example Answer:The diagram shows part of an experimental fusion reactor - Scottish Highers Physics - Question 8 - 2016

Step 1

Explain why energy is released in this reaction.

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Answer

Mass is converted into energy during the reaction. As the reactants combine to form the products, there is a loss of mass, and according to the mass-energy equivalence principle (E=mc²), this lost mass is converted into energy which is released.

Step 2

Calculate the energy released in this reaction.

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Answer

First, we calculate the total mass of the reactants and products:

  • Mass of Reactants:

    • ( m_{reactants} = 3.3436 \times 10^{-27} + 5.0083 \times 10^{-27} )
    • ( m_{reactants} = 8.3519 \times 10^{-27} \text{ kg} )
  • Mass of Products:

    • ( m_{products} = 6.6465 \times 10^{-27} + 1.6749 \times 10^{-27} )
    • ( m_{products} = 8.3214 \times 10^{-27} \text{ kg} )
  • Mass Defect (Δm):

    • ( Δm = m_{reactants} - m_{products} )
    • ( Δm = 8.3519 \times 10^{-27} - 8.3214 \times 10^{-27} = 3.0505 \times 10^{-29} \text{ kg} )

Using the mass-energy equivalence formula:

E=Δmc2E = Δm c^2

With the speed of light ( c = 3.00 \times 10^8 \text{ m/s} ):

E=(3.0505×1029 kg)×(3.00×108 m/s)2E = (3.0505 \times 10^{-29} \text{ kg}) \times (3.00 \times 10^8 \text{ m/s})^2 E=2.745×1012 JE = 2.745 \times 10^{-12} \text{ J}

Thus, the energy released in the reaction is approximately ( 2.75 \times 10^{-12} \text{ J} ).

Step 3

Explain why it is necessary to use a magnetic field to contain the plasma.

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Answer

Plasma can cool and lose energy if it comes into contact with the walls of the reactor, leading to a potential reaction stop. A magnetic field is necessary to confine the high-temperature plasma, preventing it from touching the walls and ensuring that the fusion process can continue effectively.

Step 4

Determine the direction of the force exerted by the magnetic field.

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Answer

The force on a positively charged particle in a magnetic field is given by the right-hand rule. If the particle enters the magnetic field as shown (assumed to be into the page), the force will be directed upwards, indicating that the resultant force is in the direction 'up the page'.

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