# IB DP Physics E.5 Fusion IB Style Question Bank HL Paper 2

### Question

(a) Identify with ticks [ $$\checkmark$$ ] in the table, the forces that can act on electrons and the forces that can act on quarks. (b) The following data is available for atomic masses for the fusion reaction
${ }_1^2 \mathrm{H}+{ }_1^3 \mathrm{H} \rightarrow{ }_2^4 \mathrm{He}+{ }_0^1 \mathrm{n}:$ (i) Show that the energy released is about 18MeV. 

(ii) Estimate the specific energy of hydrogen by finding the energy produced when $$0.4 \mathrm{~kg}$$ of $${ }_1^2 \mathrm{H}$$ and $$0.6 \mathrm{~kg}$$ of $${ }_1^3 \mathrm{H}$$ undergo fusion. 

(c) It is hoped that nuclear fusion can be used for commercial production of energy.

Outline

(i) two difficulties of energy production by nuclear fusion.

(ii) one advantage of energy production by nuclear fusion compared to nuclear fission. 

(d) Tritium $$\left({ }_1^3 \mathrm{H}\right)$$ is unstable and decays into an isotope of helium $$(\mathrm{He})$$ by beta minus decay with a half-life of 12.3 years.

(i) State the nucleon number of the $$\mathrm{He}$$ isotope that $${ }_1^3 \mathrm{H}$$ decays into.

(ii) The following diagram is an incomplete Feynman diagram describing the beta minus decay of $${ }_1^3 \mathrm{H}$$ into $$\mathrm{He}$$. Complete the diagram and label all the missing particles. (iii) Estimate the fraction of tritium remaining after one year. 

Ans:

a ) Weak nuclear: 2 ticks $$\checkmark$$
Strong nuclear: quarks only $$\checkmark$$

b( i)

$\varangle \mu »=2.0141+3.0160-(4.0026+1.008665) \ll=0.0188 u »$
OR
In MeV: $$1876.13415+2809.404-(3728.4219+939.5714475)$$
$=0.0188 \times 931.5 \text { OR }=17.512 \alpha \mathrm{MeV} » \checkmark$

ALTERNATIVE 1
$$0.40 \mathrm{~kg}$$ of deuterium is $$\ll \frac{400}{2} \times 6.02 \times 10^{23} \mathrm{w}=1.2 \times 10^{26}$$ nuclei
$${ }_\alpha 0.60 \mathrm{~kg}$$ of tritium is the same number $${ }_* \checkmark$$
So specific energy $$\alpha \frac{1.2 \times 10^{26} \times 17.51 \times 10^6 \times 1.6 \times 10^{-19}}{0.4+0.6} \rrbracket=3.4 \times 10^{14} \ll \mathrm{J} \mathrm{kg}^{-1} » \checkmark$$
ALTERNATIVE 2
$$\alpha 17.51 \times 10^6 \times 1.6 \times 10^{-19}=» 2.8 \times 10^{-12} \ll \mathrm{J} »$$
AND
\begin{aligned} & \ll(2.0141+3.0160) \times 1.66 \times 10^{-27}=» 8.35 \times 10^{-27} \\ & \ll \frac{2.8 \times 10^{-12}}{8.35 \times 10^{-37}},=3.4 \times 10^{14} \ll \mathrm{Jkg}^{-1} \end{aligned}

c i Requires high temp/pressure
Must overcome Coulomb/intermolecular repulsion
Difficult to contain / control «at high temp/pressurew
Difficult to produce excess energy/often energy input greater than output / OWTTE $$\checkmark$$
Difficult to capture energy from fusion reactions
Difficult to maintain/sustain a constant reaction rate

ii ) Plentiful fuel supplies $$O R$$ larger specific energy $$O R$$ larger energy density $$O R$$ little or no «major radioactive» waste products

d i ). 3

ii ) Proton shown
W- shown
Produces electron $$/ \mathrm{e}^{-} / \beta^{-}$$and antineutrino $$/ \bar{v}$$ with proper arrow directions.

iii ) \begin{aligned} & \lambda=\ll \frac{\ln 2}{12.3} \rightsquigarrow 0.056 \kappa y^{-1} » \text { OR } 0.5^{\frac{1}{m}} \text { OR } e^{-1 \times \frac{\ln 2}{12.3}} \\ & 0.945 \text { OR } 94.5 \%\end{aligned}

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