IB Physics SL E.5 Fusion and stars questions

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Question 1

Multiple choiceMedium1 mark

An HR diagram for stars P and Q is shown. Their unequal stellar parallaxes, measured in arc-seconds, are pPp_P and pQp_Q respectively. Which expression gives dred giant/dwhite dwarfd_{\text{red giant}}/d_{\text{white dwarf}}

252015105010-310-210-11101001000Surface temperature, T / 103 KLuminosity, L/LsunPQ
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Answer: C. On the HR diagram, P is cool and luminous, so it is a red giant; Q is hot and faint, so it is a white dwarf. Using d (pc)=1/p (arc-second)d\text{ (pc)}=1/p\text{ (arc-second)}

dred giantdwhite dwarf=1/pP1/pQ=pQpP.\frac{d_{\text{red giant}}}{d_{\text{white dwarf}}} =\frac{1/p_P}{1/p_Q} =\frac{p_Q}{p_P}.

A: Uses the parallax ratio directly, as though distance were proportional to parallax.
B: Reverses the required ratio and adds an unnecessary square.
D: Squares the correct inverse-parallax ratio.

Remember: distance and parallax are inversely proportional.

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