#### Back

# Hint

I(0) is proportional to Σ(_{i}ΔSLD_{i} V_{i})^{2},

where ΔSLD_{i} = SLD_{i} - SLD_{solvent} is the contrast (or excess scattering length density) of subunit i, and V_{i} is the volume of subunit i (the subunits of a core-shell particles are the the core and the shell).

In this problem, ΔSLD_{core} = -ΔSLD_{shell}, so the volumes of the core and shell must be equal to get I(0)=0. Volume of the shell: 4π(R_{outer}^{3}-R_{core}^{3})/3

Set this equal to the volume of the core, 4πR_{core}^{3}/3, and find a relation between the radii, i.e. determine the ratio = R_{outer}/R_{core}=?