24P2Q08

8a)

87.7 years is >6 times the lifespan of Perseverance.

The RTG can provide a fairly constant power over the lifespan of Perseverance.

8b)

The penetrating power of α-particles is very low. It is much easier to provide shielding so that the other devices in Perseverance are not damaged by the radiation.

8c)

α-particles are highly ionising and can cause biological damage through direct and indirect effects.

8di)

\displaystyle _{94}^{238}Pu\to _{92}^{234}U+_{2}^{4}\alpha

8dii)

Increase in total BE
\displaystyle \begin{aligned}&=(234\times 7.601+4\times 7.074)-238(7.568) \\&=1806.93-1801.184 \\&=5.746\text{ MeV}\div 1.60\times {{10}^{-19}}\div {{10}^{6}} \\&=9.19\times {{10}^{-13}}\text{ J}  \end{aligned}

8diii)

\displaystyle n{{N}_{A}}=\frac{4.9}{276\times {{10}^{-3}}}\times (6.02\times {{10}^{23}})=1.07\times {{10}^{25}}

8div)

\displaystyle \begin{aligned}A&=\lambda N \\&=\frac{\ln 2}{87.7\times 365\times 24\times 3600}(1.07\times {{10}^{25}}) \\&=2.682\times {{10}^{15}}\text{ Bq}  \end{aligned}

\displaystyle \begin{aligned}P&=(2.682\times {{10}^{15}})\times 9.19\times {{10}^{-13}} \\&=2460\text{ W}  \end{aligned}

8v)

\displaystyle _{94}^{238}Pu\to _{82}^{206}Pb+a_{2}^{4}\alpha +b_{-1}^{0}\beta

\displaystyle a=\frac{238-206}{4}=8

\displaystyle 94=82+8\times 2-b\text{ }\Rightarrow \text{ }b=4

\displaystyle _{94}^{238}Pu\to _{82}^{206}Pb+8_{2}^{4}\alpha +4_{-1}^{0}\beta

8 alpha decays and 4 beta decays.

8ei)

A decrease which decreases by a fixed percentage for the same duration of time.

8eii)

Method 1

\displaystyle \begin{aligned}P&={{P}_{o}}{{(100\%-0.79\%)}^{14}}\\&=110{{(0.9921)}^{14}} \\&=98.4\text{ W}  \end{aligned}

Method 2

\displaystyle \begin{aligned}P&={{P}_{0}}{{(\frac{1}{2})}^{\frac{14}{87.7}}} \\&=110{{(\frac{1}{2})}^{\frac{14}{87.7}}} \\&=98.5\text{ W}  \end{aligned}

8f)

\displaystyle \begin{aligned}e.m.f.&=\Delta S\Delta T \\&=(240-(-200))\times {{10}^{-6}}(1273-573) \\&=0.308\text{ V}  \end{aligned}

8g)

\displaystyle \begin{aligned}g&=\frac{GM}{{{R}^{2}}} \\\frac{{{g}_{E}}}{{{g}_{M}}}&=\frac{{{M}_{E}}}{{{M}_{M}}}\div {{(\frac{{{R}_{E}}}{{{R}_{M}}})}^{2}} \\\frac{9.81}{{{g}_{M}}}&=9.30\div {{1.88}^{2}} \\{{g}_{M}}&=3.73\text{ N k}{{\text{g}}^{-1}}  \end{aligned}

8hi)

The RTG can store the energy in some rechargeable batteries, which in turn provide the power for MOXIE.

8hii)

The operation lasts 12400 s.

Energy needed by MOXIE\displaystyle =Pt=300\times 12400=3.72\text{ MJ}

Time taken for RTG to store this amount of energy \displaystyle =\frac{3.72\times {{10}^{6}}}{110}=33818\text{ s}\div 3600=9.39\text{ hrs}

8hiii)

\displaystyle \begin{aligned}pV&=nRT \\(610)V&=\frac{5.37}{32}(8.31)(273.15-60) \\V&=0.487\text{ }{{\text{m}}^{3}}  \end{aligned}

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