Study Material

# Nanometer: equivalences, uses and examples, exercises

The nanometerÂ is a submultiple of the meter that equals 1 x 10Â -9Â m and is abbreviated 1nm.Â It represents one billionth of a meter, a scale that is not commonly handled in everyday life.

As examples: a sugar molecule is 1 nm wide, while the SARS CoV 19 virus is between 100 and 160 nm in diameter.

The word nanometer derives from the combination of two Greek words: “nanos” which means dwarf, and “metron”, or measurement standard.Â The nano prefix has become very popular recently, thanks to the rise of miniaturization and technology related to extremely small objects, such as electronic components.

These very small technologies made it possible in a short time, among other things, to create electronic devices with large computing capabilities in a portable size.Â And it also lowered costs, making them affordable for many more people.

Medical science has also benefited from this miniaturization.Â That is why it was necessary to create appropriate units of measurement to express very small sizes, including the nanometer.

## Equivalences

The following are equivalences between the nanometer and other units of measurement often used in science and engineering and give a good idea of â€‹â€‹how small this unit is:

### Nanometer to meter

The meter is the unit of length of the International System of Units SI.Â In this case the equivalence is:

1nm = 1 x 10Â -9Â m

Similarly, 1 meter has 1,000,000,000 nm, that is, one billion nanometers.

### Nanometer to cm

The centimeter is a submultiple of the meter widely used to measure everyday objects.Â The equivalence between centimeter and nanometer is:

1nm = 1 x 10Â -7Â cm

There are no less than 10 million nanometers in a centimeter.

### Nanometer to millimeter

In millimeters, a unit that is used a lot to express small things like the gauges of copper wires, for example, a nanometer is:

1nm = 1 x 10Â -6Â mm

Or what is the same, 1 nm is one millionth of a millimeter.Â It means that there are 1 million nanometers in 1 mm.

### Nanometer to microns

The micron or micrometer, abbreviated Î¼m, is another submultiple of the meter that is used for things not visible to the naked eye.Â The micron is one millionth of 1 meter, therefore:

1 nm = 0.001 Î¼m

To get an idea of â€‹â€‹these sizes: a blood cell has an approximate diameter of 10 microns, which according to the given equivalence would be 10,000 nm.Â And a bacterium is 10 times smaller still, it can measure 1 micron or 1000 nm.

### Nanometer to Picometer

The picometer, or pm, is a submultiple of the meter even smaller than the nanometer.Â One picometer equals 1 Ã— 10Â -12Â m.

1 nm = 1000 pm

Picometers are suitable for measuring very small wavelengths, such as X-rays, for example, which are on the order of about 5 pm.

## Applications of the nanometer

The nanometer is the appropriate unit of measurement for sizes in nanoscience: the so-calledÂ nanoscaleÂ or nanoscopic scale, as well as for wavelengths in the area of â€‹â€‹the electromagnetic spectrum that goes from the near infrared, through the visible spectrum to the gamma rays.

### Nanoscale

In nanoscience, which consists of the study and development of nanostructures, the ranges go from 1 to 100 nanometers, so the nanometer is an appropriate unit for the sizes that are handled there.

At this scale, gravity is not a relevant force, since the masses are very small, but other interactions take their place and it is necessary to start taking quantum effects into account.

In this way, the properties of materials at the nanoscopic level differ markedly from those at the macroscopic scale.

### Computer chips

Computer chips have been getting smaller over time.Â By the late 1980s, they could be about 2000 nanometers (0.0002 cm).Â In 2009 they were 22 nanometers and today their size has been reduced to 10 nanometers.Â They are expected to fall further, at least to half of the latter value.

### Wavelength of the visible spectrum

The electromagnetic spectrum consists of the continuum of wavelengths and frequencies in which electromagnetic waves propagate.Â They range from radio waves, the least energetic, to X-rays and gamma rays, the highest energy.

In the middle is the range of visible light: the set of wavelengths to which the human eye is sensitive.

The nanometer is a very appropriate unit of measurement for these wavelengths.Â These are the values â€‹â€‹that distinguish people:

-Red: 700 nm

-Orange: 665 nm

-Yellow: 630 nm

-Green: 600 nm.

-Blue: 550 nm.

-Indigo: 470 nm.

-Violet: 450 nm.

Wavelengths beyond red are known asÂ infraredÂ , while after violet isÂ ultravioletÂ radiationÂ .Â TheÂ SunÂ emits electromagnetic radiation mainly at all these wavelengths.

### Polarizing sheets

Polarizing films were invented in the late 1920s by the American Edwin Herbert Land (1909-1991).Â The manufacture of sunglasses is one of its best known uses.

The material used consists of long chains of hydrocarbon molecules coated with iodine and arranged in parallel rows, the separation of which is less than the wavelength of the light to be filtered.

Therefore the separation must be around a few hundred nanometers.

The conduction electrons in the molecules are mobile throughout the chain, which in this way behaves just like a very fine conductive wire.

In this way, when nonpolarized light falls on the sheet (which contains both vertically and horizontally polarized components), these electrons begin to oscillate horizontally along the chain.

The result is a linearly polarized wave, with a phase difference of 180Âº with respect to the horizontal component of non-polarized light, which cancel each other out.Â Thus, the polarizing sheet absorbs said horizontal component, letting only the vertical one pass.

### Light diffraction

For the diffraction of light to occur, the size of the gratings must be of the order of nanometers, since the diffraction only occurs if the dimension of the obstacle is less than the incident wavelength.

## Training

Transform the following measurements into nanometers:

a) 0.000056 cm

b) 4 microns

c) 200 pm

d) 40.3 mm

e) 0.0027 dm

#### Solution to

0.000056 cm = 0.000056 cm x 1 x 10Â 7Â nm / cm = 560 nm

#### Solution b

4 microns = 4 microns x 1000 nm / Î¼m = 4000 nm

#### Solution c

200 pm = 200 pm x 0.001 nm / pm = 0.2 nm

#### Solution d

40.3 mm = 40.3 mm x 1 x 10Â 6Â nm / mm = 40.3 x 10Â 6Â nm

#### Solution e

A dm is a decimeter, or tenth of a meter:

0.0027 dm = 0.0027 dm x 1 x 10Â 8Â nm / dm = 270000 nm

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