Question

How is the unit of measurement, a nanometer related to an angstrom? Explain.

Answer 1

Hint: To find the relation between a nanometer and an angstrom we express them in terms of a common unit of measurement like meters and make a relation between them.

Step By Step Answer :
A nanometer is a unit of measurement length in the metric system which is one billionth of the standard unit of measurement “meter”.

It is denoted by ‘nm’.

It can be expressed as 1 nanometer = $1\times {10}^{-9}$m. --- (1)

It is a part of the S.I system of units.

A nanometer is generally used to measure very small distances like the size of molecules or while observing germs under an electronic microscope.

An angstrom is a unit of measurement length in the metric system which is one ten-billionth of the standard unit of measurement “meter”.

It is denoted by${}^{\prime }{\stackrel{\text{o}}{\text{A}}}^{\prime }$.

It can be expressed as 1 angstrom = $1\times {10}^{-10}$m. --- (2)
It is not a part of the S.I system of units.

An angstrom is generally used to measure very small distances like the wavelength of a light wave etc.

Therefore from equation (1) and (2), we get
$\text{1m = }{10}^{\text{9}}\text{nm = 1}{\text{0}}^{10}\stackrel{\text{o}}{\text{A}}$

$$\begin{gathered} \Rightarrow {10}^{\text{9}}\text{nm = 1}{\text{0}}^{10}\stackrel{\text{o}}{\text{A}} \\ \Rightarrow 1\text{ nm = 10 }\stackrel{\text{o}}{\text{A}} \end{gathered}$$


Hence the relation between a nanometer and an angstrom is that one nanometer is equal to ten times of an angstrom.

Note: In order to solve this type of questions the key is to know the definitions of angstrom and nanometer. Once we know the definition we write it in terms of a single unit and form a relation between them.
Just like angstrom and nanometers are units of distance for very small measurements, there are a few units which are used to measure very long distances. They are –
Nautical mile, it is a measurement used in marine and space navigation. 1 nautical mile = 1852 m.
Light year, it is defined as the distance a light ray travels in one year. 1 light year = 9.4607 × ${10}^{12}$ Km.