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Question: 1 fermi is equal to A. \({{10}^{-15}}m\) B. \({{10}^{-9}}micron\) C. \({{10}^{-5}}{{A}^{\circ ...

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

Explanation

Solution

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{{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{{10}^{-6}} metre ---- (i)
1 Fermi = 10−15{{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 = 10−1510−6\dfrac{{{10}^{-15}}}{{{10}^{-6}}} micron.
= 10−15+6{{10}^{-15+6}} micron
= 10−9{{10}^{-9}} micron.
Next, to compare one fermi with 1 A∘{{A}^{\circ }}.
1 A∘{{A}^{\circ }} = 10−10{{10}^{-10}} metre. ------ (iii)
1 Fermi = 10−15{{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∘{{A}^{\circ }}.
i.e. Divide ‘iv’ by ‘iii’
⇒\Rightarrow 1 Fermi = 10−1510−10A∘\dfrac{{{10}^{-15}}}{{{10}^{-10}}}{{A}^{\circ }}
= 10−15+10A∘{{10}^{-15+10}}{{A}^{\circ }}
= 10−5A∘{{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.