How small is a nanoparticle?
A nanometre is one billionth of a metre: 1 nm = 1 × 10⁻⁹ m. An atom is about 0.1 nm wide, so a nanoparticle (1–100 nm) contains only a few hundred to a few thousand atoms.
Scientists group particles by diameter:
- Coarse particles (PM10): 1 × 10⁻⁵ m to 2.5 × 10⁻⁶ m (dust, pollen).
- Fine particles (PM2.5): 2.5 × 10⁻⁶ m to 1 × 10⁻⁷ m (smoke, car exhaust).
- Nanoparticles: 1 × 10⁻⁷ m to 1 × 10⁻⁹ m.
To compare sizes, divide: a 100 nm particle is 10 times wider than a 10 nm particle. Each jump of one power of ten (one 'order of magnitude') means ×10.
Surface area to volume ratio
For a cube of side s: surface area = 6s², volume = s³, so the surface area : volume = 6 ÷ s.
When the side gets 10 times smaller, the ratio gets 10 times bigger. A 1 cm cube has ratio 6 : 1 (per cm). A 10 nm cube has ratio 6 000 000 : 1. So in a nanoparticle a big fraction of atoms are on the surface, where reactions happen.
That is why nanoparticles can behave differently from the same substance in bulk. For example, bulk gold is unreactive and shiny yellow, but gold nanoparticles can look red and act as catalysts. Because more surface is exposed, a smaller mass of nanoparticle catalyst can do the same job as a lot of bulk catalyst.
Uses of nanoparticles
- Sunscreens and cosmetics: nano zinc oxide and titanium dioxide block UV light but look clear on skin.
- Medicine: carrying drugs to exactly the right cells, and in tests and bandages.
- Germ killers: silver nanoparticles in socks, wound dressings and some water filters kill bacteria.
- Catalysts: huge surface makes reactions faster, for example in car exhaust converters.
- Electronics and materials: carbon nanotubes and nanoparticles make tiny circuits and strong, light sports equipment.
Possible risks
Because they are so small, nanoparticles may be breathed in deep into the lungs, pass into cells or travel through the body. Fine PM2.5 air pollution is already linked to lung and heart disease. Silver nanoparticles washed out of clothes may harm useful bacteria in rivers. Scientists are still studying long-term effects, so new nano products need careful testing and clear labels.
Try it: sugar race
Take two glasses of the same cold water. Drop one sugar cube into the first and the same amount of powdered sugar into the second. Stir both the same way and time how long each takes to disappear. The powder wins because cutting the cube made much more surface touch the water. Then cut the cube in the 3D and watch the surface area climb.
Key formulas and definitions
- 1 nm = 1 × 10⁻⁹ m; nanoparticles are 1–100 nm
- Cube: surface area = 6s², volume = s³
- Surface area : volume = 6 ÷ s (for a cube)
- Side ÷ 10 → surface area to volume ratio × 10
- PM10: 2500–10 000 nm; PM2.5: 100–2500 nm
Worked examples
1. Find the surface area to volume ratio of a cube with side 2 cm.
SA = 6 × 2² = 24 cm². V = 2³ = 8 cm³. Ratio = 24 ÷ 8 = 3 : 1 (per cm). Check: 6 ÷ s = 6 ÷ 2 = 3.
2. A cube of side 1 cm is cut into cubes of side 1 mm. By how many times does the total surface area increase?
1 mm = 0.1 cm, so the side is 10 times smaller. The volume stays 1 cm³, so the ratio (and the total surface area) becomes 10 times bigger: 6 cm² → 60 cm².
3. Write 50 nm in metres in standard form.
50 nm = 50 × 10⁻⁹ m = 5 × 10⁻⁸ m.
4. A nanoparticle is 20 nm wide and a fine particle is 2000 nm wide. How many times wider is the fine particle? How many orders of magnitude?
2000 ÷ 20 = 100 times wider = 10², so 2 orders of magnitude.
Common mistakes
- Thinking that cutting a cube changes its total volume. Only the surface area grows.
- Mixing nm and µm: 1 µm = 1000 nm, and 1 nm = 10⁻⁹ m (not 10⁻⁶ m).
- Saying nanoparticles are a new element. They are ordinary substances in very tiny pieces.
- Writing the ratio upside down. Surface area to volume means SA ÷ V, and it gets bigger as particles get smaller.