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Question: 1 millimeter = ______ picometer \[ A.{\text{ }}{10^9} \\\ B.{\text{ }}{10^{ - 9}} \\\ ...

1 millimeter = ______ picometer

A. 109 B. 10−9 C. 108 D. 1010  A.{\text{ }}{10^9} \\\ B.{\text{ }}{10^{ - 9}} \\\ C.{\text{ }}{10^8} \\\ D.{\text{ }}{10^{10}} \\\
Explanation

Solution

Hint: In order to deal with this question first we will know about the process to measure a picometer then we write the picometer in terms of meter , further we will convert this meter in millimeter. In this way by taking a meter as the reference or the link between millimeter and picometer we will find the relation between them.

Formula used- 1mm=10−3m,1pm=10−12m1mm = {10^{ - 3}}m,1pm = {10^{ - 12}}m

Complete step-by-step solution -

In order to find the relation between picometer and millimeter we will first see their relation with standard unit of length i.e. meter
As we know that
1 picometer =10−12 = {10^{ - 12}} meter
And 1 millimeter =10−3 = {10^{ - 3}} meter ---- (1)
Now let us find the meter in terms of the picometer from the above relation.
∵1pm=10−12m ⇒1m=1pm10−12 ⇒1m=1012pm..........(2)  \because 1pm = {10^{ - 12}}m \\\ \Rightarrow 1m = \dfrac{{1pm}}{{{{10}^{ - 12}}}} \\\ \Rightarrow 1m = {10^{12}}pm..........(2) \\\
As we have the relation between millimeter and meter in equation (1) and the relation between meter and picometer and meter in equation (2) using the above two relation let us proceed to find the relation by substituting equation (2) into equation (1).
∵1mm=10−3m ⇒1mm=10−3×1m ⇒1mm=10−3×(1012pm) [∵1m=1012pm] ⇒1mm=109pm  \because 1mm = {10^{ - 3}}m \\\ \Rightarrow 1mm = {10^{ - 3}} \times 1m \\\ \Rightarrow 1mm = {10^{ - 3}} \times \left( {{{10}^{12}}pm} \right){\text{ }}\left[ {\because 1m = {{10}^{12}}pm} \right] \\\ \Rightarrow 1mm = {10^9}pm \\\
Hence, 1 millimeter =109 = {10^9} picometer

So, the correct answer is option A.

Note- The atomic radii and the distances between atomic nuclei and electrons are usually the only things measured in picometers. The distance between atoms is usually discussed in angstroms (= 100 picometers), and femtometers (= 0.001 picometers) are used to discuss nuclear diameters. In the International System of Units, the meter or meter is the base unit length. The symbol for unit SI is m. The meter is known as the length of the track that light travels in a second vacuum.