| English | 意味 |
|---|---|
| nuclear fusion/ˈnjuːklɪə ˈfjuːʒn/ | 核融合 |
| nuclear fission/ˈnjuːklɪə ˈfɪʃn/ | 核分裂 |
| kinetic energy/kɪˈnetɪk ˈenədʒi/ | 運動エネルギー |
| electrostatic/ɪˌlektrəʊˈstætɪk/ | 静電気 |
| strong nuclear force/strɒŋ ˈnjuːklɪə fɔːs/ | 強相互作用 |
| chain reaction/tʃeɪn rɪˈækʃn/ | 連鎖反応 |
| critical mass/ˈkrɪtɪkl mæs/ | 臨界質量 |
Two opposite processes, one rule
- Joining two tiny nuclei releases energy. Splitting one enormous nucleus releases energy. Those sound like contradictory statements.
- They are not, because both are the same move: climbing the binding-energy-per-nucleon curve towards its peak.
- A nucleus already sitting at the peak, iron-56, can release energy by neither process. That is where a star's fusion stops.
- This lesson is nuclear fusion 核聚变, nuclear fission 核裂变, and how to calculate what they give out.
Both arrows point at iron
Why moving towards the peak releases energy
- On the curve, a higher position means each nucleon is more tightly bound.
- In both processes the products lie higher than the reactants, so the total binding energy increases.
- That extra binding energy is released, as the kinetic energy of the products and as photons.
- Equivalently, the total mass of the products is less than that of the reactants, by exactly $\Delta E/c^2$. Those are two descriptions of one event, and an answer wants both.
核分裂鎖状反応
中性子が高い質量の原子核を分裂させ、エネルギーとより多くの中性子を放出する—その中性子がさらに他の原子核を分裂させる。
Energy is released when nuclei move:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Climbing the B/A curve toward iron means the products are more tightly bound, so energy is released.
Put the explanation of why fusion and fission both release energy in order.
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
The mass loss and the binding-energy gain are the same event described two ways, and a full answer says both.
An iron-56 nucleus can release energy by either fusion or fission.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
It sits at the peak, so every move takes it DOWN the curve and would need energy put in. This is why fusion inside a star stops at iron.
Fusion
- Fusion joins two light nuclei into one heavier nucleus:
- The product has greater binding energy per nucleon than the reactants, so energy comes out. This is what powers every star.
- It needs millions of kelvin, and the reason is specific: the nuclei are both positive, so they must have enough kinetic energy 动能 to overcome their electrostatic 静电 repulsion and get close enough for the strong nuclear force 强核力 to take over.
- "It needs high temperature" alone is half an answer. Name the repulsion being beaten and the force taking over.
Fusion needs very high temperatures to overcome the electrostatic repulsion between nuclei.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The nuclei must get close enough for the strong force to act, despite repelling — hence the millions of kelvin in stars.
Why does fusion need millions of kelvin? Select all that apply.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
"It needs high temperature" is half an answer. Name the electrostatic repulsion being beaten and the strong nuclear force taking over.
Fission
- Fission splits a heavy nucleus into two lighter ones, usually after it absorbs a neutron:
- The products sit higher on the curve than uranium-235, so energy is released.
- The extra neutrons can trigger further fissions: a chain reaction 链式反应, which sustains itself only in a large enough mass of fuel, the critical mass 临界质量.
- Below the critical mass too many neutrons escape from the surface before finding a nucleus, and the reaction dies out.
One neutron in, three out
The extra neutrons released in fission can trigger a ____ reaction.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Each fission releases neutrons that cause more fissions — a chain reaction in a critical mass of fuel.
A sustained chain reaction needs a critical mass of fuel.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Below the critical mass too many neutrons escape, and the reaction dies out.
The marked contrast
- Fission: a heavy nucleus, large $A$, splits into two lighter nuclei of roughly similar mass, usually after absorbing a neutron, and releases further neutrons.
- Fusion: two light nuclei, small $A$, join into one heavier nucleus, and it needs very high temperature and pressure to overcome the electrostatic repulsion.
- Both release energy, but per kilogram of fuel, fusion releases more.
- Write the contrast in matched pairs: heavy against light, splits against joins, absorbs a neutron against needs high temperature. A list of facts about only one of them scores half.
Match each process to what it does.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Both move toward the iron peak, so both can release energy.
Match each feature to the process it describes.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Write the contrast in matched pairs. A list of facts about only one process collects half the marks.
Worked example: energy from a mass change
- In a nuclear reaction the total mass decreases by $0.020\ \text{u}$. Find the energy released.
- $\Delta E = \Delta m\,(\text{u}) \times 931 = 0.020 \times 931 = 19\ \text{MeV}$.
- The recipe is always the same four moves: total mass of reactants, total mass of products, $\Delta m = m_{\text{reactants}} - m_{\text{products}}$, then $\Delta E = c^2\Delta m$.
- A positive $\Delta m$ means energy is released. If you get a negative answer you have subtracted the wrong way round, not discovered a reaction that absorbs energy.
A reaction has a mass change of $0.020\ \text{u}$. How much energy is released, in MeV?
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
$\Delta E = \Delta m\,(\text{u}) \times 931 = 0.020 \times 931 \approx 18.6\ \text{MeV}$.
Worked example: fusing two deuterium nuclei
- The mass defect of $^{2}_{1}\text{H}$ is $0.002388\ \text{u}$ and that of $^{4}_{2}\text{He}$ is $0.030377\ \text{u}$. Find the energy released when two deuterium nuclei fuse into one helium-4 nucleus.
- Work with binding energies, since mass defects are given. Before: $2 \times 0.002388 = 0.004776\ \text{u}$ of defect. After: $0.030377\ \text{u}$.
- The defect has increased by $0.030377 - 0.004776 = 0.025601\ \text{u}$, and an increase in mass defect is energy given out.
- $\Delta E = 0.025601 \times 931 = 23.8\ \text{MeV}$.
- Note the shape of it: you may work either from the masses of the nuclei or from their mass defects, but never mix the two in one sum.
Two deuterium nuclei (mass defect 0.002388 u each) fuse into helium-4 (mass defect 0.030377 u). How much energy is released, in MeV? (931 MeV per u.)
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
The mass defect increases by 0.030377 - 2(0.002388) = 0.025601 u, and an increase in defect is energy released: 23.8 MeV. Work from masses OR from defects, never a mixture.
Marks that slip away
- Explaining the energy release needs the curve: the products are higher, so the total binding energy increases and mass is lost.
- For fusion, name what the temperature is for: overcoming electrostatic repulsion so the strong nuclear force can act.
- A chain reaction needs a critical mass, otherwise too many neutrons escape.
- Fission usually absorbs a neutron first and releases more. Say how many if the equation shows them.
- Iron-56 releases energy by neither process. That is a fact worth a mark, and it is the reason stellar fusion stops there.
You've got it
- energy is released whenever nuclei move towards the iron peak, because the products are more tightly bound and the total mass falls by $\Delta E/c^2$
- fusion joins two light nuclei and needs millions of kelvin so the nuclei can beat their electrostatic repulsion and let the strong nuclear force act
- fission splits a heavy nucleus after absorbing a neutron, releasing more neutrons that can sustain a chain reaction above the critical mass
- to find the energy: total reactant mass, total product mass, $\Delta m$, then $\Delta E = c^2\Delta m$, or $\Delta m\,(\text{u}) \times 931$ in MeV