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(Mass of electron = ${\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ kg}}$; Avogadro number, = \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}\]

(A) \[\dfrac{1}{{{\text{9}}{\text{.108 x 6}}{\text{.023 }}}}{\text{x1}}{{\text{0}}^{\text{8}}}\]

(B) \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}\]

(C) \[\dfrac{1}{{{\text{9}}{\text{.108}}}}{\text{x 1}}{{\text{0}}^{{\text{31}}}}\]

(D) \[\dfrac{{{\text{6}}{\text{.023}}}}{{{\text{9}}{\text{.108 }}}}{\text{x1}}{{\text{0}}^{54}}\]

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We know that one mole of any substance has an Avogadro number of atoms or molecules or ions. Avogadro number,\[{\text{\;}}{{\text{N}}_{\text{A}}}\]= \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}\]

⟹Mass of one mole of electrons = ${\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ x 6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}$kg

Since in the options we can see that the numbers are not in simplified form so we do not perform the multiplication we can keep it as such till the end.

Now, we need to find the number of moles of electrons that weigh one kilogram(kg)

⟹ The number of mole of electrons that weigh one kilogram = $\dfrac{1}{{{\text{9}}{\text{.108 x 1}}{{\text{0}}^{{\text{ - 31}}}}{\text{ x 6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}}}$

Now let’s just simplify the power terms, by doing so we get,

⟹The number of mole of electrons that weigh one kilogram = $\dfrac{1}{{{\text{9}}{\text{.108 x 6}}{\text{.023 x 1}}{{\text{0}}^{ - 8}}{\text{ }}}}$

⟹The number of mole of electrons that weigh one kilogram =$\dfrac{1}{{{\text{9}}{\text{.108 x 6}}{\text{.023}}}}{\text{x 1}}{{\text{0}}^8}$

\[{\text{Number of moles = }}\dfrac{{{\text{Number of particles}}}}{{{\text{Avogadro Number}}}}\]