E.3 Radioactive decay SL Paper 2- IBDP Physics 2025- Exam Style Questions

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