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Nuclear and quantum physics · Question 9
Nuclear and quantum physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
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- Marks
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- Topics
- 2
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In one fission event, a nucleus of ²³⁵U absorbs a neutron and splits, releasing about 200 MeV of energy. In the core of the Sun, four hydrogen nuclei are effectively converted into one helium-4 nucleus, releasing about 26 MeV.
- (a)
Determine Determine the energy released, in joules, per kilogram of uranium-235 undergoing fission. The mass of a ²³⁵U atom may be taken as 3.9 × 10⁻²⁵ kg.
4 marks - (b)
Explain Explain, in terms of binding energy per nucleon, why both fission of uranium and fusion of hydrogen release energy.
3 marks - (c)
Explain Explain why extremely high temperatures are required for fusion but not for fission.
3 marks - (d)
Discuss The Sun's luminosity is 3.8 × 10²⁶ W. Discuss whether the fusion of hydrogen can account for the Sun's output over its estimated remaining lifetime of about 5 × 10⁹ years.
4 marks
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(a)
Determine Determine the energy released, in joules, per kilogram of uranium-235 undergoing fission. The mass of a ²³⁵U atom may be taken as 3.9 × 10⁻²⁵ kg.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
number of nuclei per kg = 1 / 3.9 × 10⁻²⁵ = 2.56 × 10²⁴
- 2
energy per fission = 200 × 10⁶ × 1.60 × 10⁻¹⁹ = 3.2 × 10⁻¹¹ J
- 3
energy per kg = 2.56 × 10²⁴ × 3.2 × 10⁻¹¹
- 4
= 8.2 × 10¹³ J kg⁻¹
(b)
Explain Explain, in terms of binding energy per nucleon, why both fission of uranium and fusion of hydrogen release energy.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
energy is released whenever the products are more tightly bound — have a greater binding energy per nucleon — than the reactants
- 2
uranium lies to the right of the peak of the curve, so its fragments are closer to iron and more tightly bound
- 3
hydrogen lies far to the left, so helium formed from it is much more tightly bound
(c)
Explain Explain why extremely high temperatures are required for fusion but not for fission.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
fusing nuclei are both positively charged and must be brought within range of the strong nuclear force
- 2
this requires them to overcome a large electrostatic repulsion, which needs very high kinetic energies and hence very high temperatures
- 3
a neutron has no charge, so it experiences no repulsion and can enter a uranium nucleus at ordinary — even low — energies
(d)
Discuss The Sun's luminosity is 3.8 × 10²⁶ W. Discuss whether the fusion of hydrogen can account for the Sun's output over its estimated remaining lifetime of about 5 × 10⁹ years.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
total energy required = 3.8 × 10²⁶ × 5 × 10⁹ × 3.15 × 10⁷ = 6.0 × 10⁴³ J
- 2
each helium nucleus formed releases 26 MeV = 4.2 × 10⁻¹² J, using about 6.7 × 10⁻²⁷ kg of hydrogen
- 3
so the mass of hydrogen required is about 6.0 × 10⁴³ × 6.7 × 10⁻²⁷ / 4.2 × 10⁻¹² ≈ 1 × 10²⁹ kg
- 4
this is around 5% of the Sun's mass of 2 × 10³⁰ kg, and since fusion occurs only in the hot dense core rather than throughout the Sun, this is consistent with the estimated lifetime
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