Question

1 nanometer is _________ femtometer
\[
  A.{\text{ }}{10^5} \\
  B.{\text{ }}{10^6} \\
  C.{\text{ }}{10^7} \\
  D.{\text{ }}{10^4} \\
 \]

Answer 1

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

Complete step-by-step answer:

Formula used- $1nm = {10^{ - 9}}m,1fm = {10^{ - 15}}m$
In order to find the relation between femtometer and nanometer we will first see their relation with standard unit of length i.e. meter
As we know that
1 femtometer $ = {10^{ - 15}}$ meter
And 1 nanometer $ = {10^{ - 9}}$ meter ---- (1)
Now let us find the meter in terms of the femtometer from the above relation.
$
  \because 1fm = {10^{ - 15}}m \\
   \Rightarrow 1m = \dfrac{{1fm}}{{{{10}^{ - 15}}}} \\
   \Rightarrow 1m = {10^{15}}fm..........(2) \\
 $
As we have the relation between nanometer and meter in equation (1) and the relation between meter and femtometer and meter in equation (2) using the above two relation let us proceed to find the relation by substituting equation (2) into equation (1).
$
  \because 1nm = {10^{ - 9}}m \\
   \Rightarrow 1nm = {10^{ - 9}} \times 1m \\
   \Rightarrow 1nm = {10^{ - 9}} \times \left( {{{10}^{15}}fm} \right){\text{ }}\left[ {\because 1m = {{10}^{15}}fm} \right] \\
   \Rightarrow 1nm = {10^6}Fm \\
 $
Hence, 1 nanometer $ = {10^6}$ femtometer
So, the correct answer is option B.

Note: Nanometers cannot be used to measure long distances. Instead, they serve to measure extremely small objects, such as atomic or transistor structures found in modern CPUs. The distance between atoms is generally defined in angstroms (= 100 picometers), and femtometers (= 0.001 picometers) are used to analyze nuclear diameters. In the International System of Units, the meter or meter is the base unit length. The acronym for unit SI is m. The meter is known as the length of the track that light travels in a second vacuum.