Question

1 fermi is equal to
A. ${{10}^{-15}}m$
B. ${{10}^{-9}}micron$
C. ${{10}^{-5}}{{A}^{\circ }}$
D. A, B, C

Answer 1

Hint: Fermi, sometimes also referred to as Femtometer, is a unit of length in the SI unit. Find the value of all the given units in a common unit i.e. metre. Once all units are converted into metres then it is easy to compare and find the correct answer.

Complete step by step answer:

Fermi, sometimes also referred to as Femtometer, is a unit of length in the SI unit. One Fermi is a very small length. It is equal to ${{10}^{-15}}$th of a metre. Being such a small unit of length, Fermi is used in the measure of really small distances in nuclear science. A number of other units are also used to measure such tiny lengths, so let us convert the unit of fermi to the other units.
Micron/Micrometre is a similar unit of length. To compare fermi with micron, let us first convert both the units to a common unit, i.e. metre.
1 micron = ${{10}^{-6}}$ metre ---- (i)
1 Fermi = ${{10}^{-15}}$ metre ---- (ii)
To compare how much one fermi is to one micron divide the equivalent of one fermi in metre to that of one micron
i.e: Divide ‘ii’ by ‘I’
$\Rightarrow$ 1 Fermi = $\dfrac{{{10}^{-15}}}{{{10}^{-6}}}$ micron.
               = ${{10}^{-15+6}}$ micron
                             = ${{10}^{-9}}$ micron.
Next, to compare one fermi with 1 ${{A}^{\circ }}$.
1 ${{A}^{\circ }}$ = ${{10}^{-10}}$ metre. ------ (iii)
1 Fermi = ${{10}^{-15}}$ metre ----- (iv)
To compare how much one fermi is to 1 A° divide the equivalent of one fermi in meters to that of 1 ${{A}^{\circ }}$.
i.e. Divide ‘iv’ by ‘iii’
$\Rightarrow$ 1 Fermi = $\dfrac{{{10}^{-15}}}{{{10}^{-10}}}{{A}^{\circ }}$
                              = ${{10}^{-15+10}}{{A}^{\circ }}$
                        = ${{10}^{-5}}{{A}^{\circ }}$.
Hence, all first three options given are correct.
Therefore, the answer is D.

Note: Actually, all the four options are correct. We cannot say that the first three options are incorrect and only the fourth option is correct. However, it is a single answer correct question so we have to select the best-suited option. The best suited in this case is D, which says that all other three options are correct.