4. (a) Atoms, molecules, nanoparticles and protons are types of particle - Edexcel - GCSE Chemistry - Question 4 - 2023 - Paper 2

To convert nanometres to metres, we use the conversion factor:

$1 ext{ nm} = 1 imes 10^{-9} ext{ m}$

Thus,

$90 ext{ nm} = 90 imes 10^{-9} ext{ m} = 9.0 imes 10^{-8} ext{ m}$

For a cube-shaped nanoparticle with side length $s = 90 ext{ nm}$, we can first calculate the surface area and volume.

1. Surface area (SA) is given by:

   $SA = 6s^{2} = 6(90 imes 10^{-9})^{2} = 48,600 imes 10^{-18} ext{ m}^2$

2. Volume (V) is given by:

   $V = s^{3} = (90 imes 10^{-9})^{3} = 729,000 imes 10^{-27} ext{ m}^3$

3. Now, we find the surface area to volume ratio (SA:V):

   ext{Ratio} = rac{SA}{V} = rac{48,600 imes 10^{-18}}{729,000 imes 10^{-27}} = 1:15

Thus, the simplest surface area to volume ratio is 1:15.