A new sun cream has been developed using zinc oxide nanoparticles - OCR Gateway - GCSE Chemistry - Question 17 - 2019 - Paper 3

To calculate the surface area to volume ratio for a cube-shaped nanoparticle with side length 50 nm:

1. Surface Area Calculation: The surface area (SA) of a cube is given by the formula: $SA = 6s^2$ where $s$ is the length of a side.

   For our nanoparticle: $SA = 6(50 ext{ nm})^2 = 6 imes 2500 ext{ nm}^2 = 15000 ext{ nm}^2$

2. Volume Calculation: The volume (V) of a cube is given by the formula: $V = s^3$

   For our nanoparticle: $V = (50 ext{ nm})^3 = 125000 ext{ nm}^3$

3. Surface Area to Volume Ratio: Now, we can find the surface area to volume ratio: ext{ratio} = rac{SA}{V} = rac{15000 ext{ nm}^2}{125000 ext{ nm}^3} = 0.12 ext{ nm}^{-1}

DNA is considered a nanoparticle because it possesses dimensions on the nanoscale, specifically around 2.5 nm in diameter. It is a complex structure that can exhibit unique properties due to its size. In contrast, a water molecule, which has a diameter of approximately 0.27 nm, is not classified as a nanoparticle since it does not meet the criteria for size and complexity associated with nanoparticles, which typically range from 1 nm to 100 nm.

To determine how many zinc oxide nanoparticles (with a diameter of 32 nm) would fit across a human hair (which has an approximate diameter of 100,000 nm):

1. Human Hair Diameter: Approximately 100,000 nm.

2. Nanoparticle Diameter: 32 nm.

3. Number of Nanoparticles: Number of nanoparticles across a human hair = rac{ ext{Diameter of Human Hair}}{ ext{Diameter of Nanoparticle}} = rac{100000 ext{ nm}}{32 ext{ nm}} = 3125

Thus, approximately 3100 zinc oxide nanoparticles would fit across a human hair when rounded to two significant figures.