Solution
= Solution
The coherent <neutron scattering length density> is atomic number density times scattering length:
$$
\rho_b^{Si}=\frac{2.33\times10^6}{28}
(6.022\times10^{23})(4.15\times10^{-15})
=2.080\times10^{14}\,\mathrm{m^{-2}}
=\boxed{2.080\times10^{-6}\,\mathrm{\mathring A^{-2}}}.
$$
The density was converted to $\mathrm{g\,m^{-3}}$ to match the molar mass in grams per mole, and $1\,\mathrm{m^{-2}}=10^{-20}\,\mathrm{\mathring A^{-2}}$.