IB Physics HL E.1 Structure of the atom questions

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Question 1

Multiple choiceMedium1 mark

The schematic shows two spherical nuclei. Assume that all nucleons have the same mass. Each option gives RX/RYR_X/R_Y and ρX/ρY\rho_X/\rho_Y respectively. Which row is correct?

Nucleus Xnucleon number A=8RXNucleus Ynucleon number A=64RY
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Answer: C. The nuclear radius relation is R=R0A1/3R=R_0A^{1/3} From the figure, RX/RY=(8/64)1/3=1/2R_X/R_Y=(8/64)^{1/3}=1/2 The mass ratio is 1/81/8 and the spherical volume ratio is (1/2)3=1/8(1/2)^3=1/8 so ρX/ρY=(1/8)/(1/8)=1\rho_X/\rho_Y=(1/8)/(1/8)=1

A: uses the mass ratio as the density ratio, omitting the volume comparison.
B: reverses the radius ratio, although its density ratio is unity.
D: treats the masses as equal and uses the inverse volume ratio, giving 88
Remember: nuclear mass and volume both scale with nucleon number, so nuclear density is constant.

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