Question

The mass of an electron is \[9.11{\text{ }}X{\text{ }}{10^{ - 31}}kg\]. How many electrons would 1 milligram make?

Answer 1

Hint: We have to convert the mass from kg to milligram and then use it to find the number of electrons in 1 milligram of electrons.


Complete step by step solution:
We are given that the mass of the electron is \[9.11{\text{ }}X{\text{ }}{10^{ - 31}}kg\].
First, we will convert this mass from kg to milligram for easier calculation in later parts.
We know that one kilogram is equal to thousand grams and one gram is equal to thousand milligrams. So, one kilogram will be equal to:
1kg= $1000 \times 1000 = {10^6}$milligram
So now, mass of an electron in milligram will be
$9.11 \times {10^{ - 31}}{\text{kg}} \times {\text{1}}{{\text{0}}^6} = 9.11 \times {10^{ - 25}}{\text{milligram}}$
We are given 1 milligram of electron, we know
1 electron is equal to \[9.11{\text{ }}X{\text{ }}{10^{ - 25}}milligrams\], so
1 milligram will be equal to $\dfrac{1}{{9.11 \times {{10}^{ - 25}}}}$ electron which will be equal to\[1.09{\text{ }}X{\text{ }}{10^{24}}\].
So, \[1.09{\text{ }}X{\text{ }}{10^{24}}\] electrons will make the total of 1 milligram.
Additional Information:
Electrons are the negatively charged species that revolves around the nucleus of an atom.
Nucleus consists of protons and neutrons.
Electrons are the one that participates in the interaction between two atoms and bond forming.
More the distance between nucleus and electrons, lower the interaction between them and easier the removal of electrons.

Note: We have to know that electrons have the smallest mass considering the three species residing in atoms (electron, proton and neutron). Proton and neutron are having almost similar weights. Hence, whenever we calculate the mass of an atom we usually neglect the mass of electrons.