Question

The wavelength of light is $589nm$. What is its order of magnitude in metres?

Answer 1

Hint: The given wavelength is a very small quantity and hence a very small unit is used to represent its magnitude. The prefix before the meter helps us understand how many parts of a metre do the unit represents. The order of magnitude is the base 10 part of the given number.

Complete answer:
The wavelength of light is defined as the distance between two identical points on a wave. Its SI unit is metre.
Distance can be expressed in many other units other than metres. A prefix is added before metre to represent parts of a metre. For example, a kilometer is ${{10}^{3}}$ parts of a meter. Therefore,
$1km=1000m$
Given, wavelength is $589nm$
Nanometer or nm represents ${{10}^{-9}}$ parts of a meter. Therefore,
$1nm={{10}^{-9}}nm$
So, $589nm$ will be
$589nm=589\times {{10}^{-9}}m$
$\Rightarrow 589nm=5.89\times {{10}^{-7}}m$ - (1)
The order of magnitude of a number is the size of it represented in base ten units. Therefore, the order of magnitude is the part of the number in base ten units. From eq (1), the order of magnitude of $589nm$ is ${{10}^{-7}}$.
Therefore, the order of magnitude of $589nm$ is ${{10}^{-7}}$.

Additional Information:
A wave is a disturbance in space. It propagates from one point to another in space by transmitting its energy forward. Waves are of two types; transverse waves and electromagnetic waves. Transverse waves require a medium to travel while electromagnetic waves do not require a medium. Properties used to describe a wave are wavelength, frequency, amplitude etc.

Note:
In order to calculate the order of magnitude, the number must be written according to the rules of scientific notation first. According to different unit systems, distance has different units. The most common system used around the world is the SI system. Other systems include the metric system, the CGS system, the imperial system etc.