Question

Answer the following questions.
(I) Calculate the number of electrons which will together weigh one gram.
(II) Calculate the mass and charge of one mole of electrons.

Answer 1

Hint: We already know the mass of one electron is $9.11\times {10}^{-31}kg$ and charge of one electron is $1.602\times {10}^{-19}C$. Find the no. of electrons which together weighs one gram using the mass of one electron. One mole is also known as Avogadro number. Avogadro number is $6.023\times {10}^{23}$. So find the mass and charge of Avogadro number of molecules using mass and charge of an electron.

Complete Step by step answer: We are given to find the no. of electrons which will together weigh one gram; mass and charge of one mole of electrons.
Electrons are one of the three main particles (protons, electrons, neutrons) of an atom. Electrons are negatively charged particles. Every atom will have equal no. of protons and electrons. Electrons get attracted to protons which are present at the centre of an atom.
 (i) Number of electrons which together weigh one gram.
We already know the mass of an electron which is $9.11\times {10}^{-31}kg=9.11\times {10}^{-28}g$
1 electron weighs $9.11\times {10}^{-28}g$
X electrons weigh 1 g.
We have to calculate x.
$$\begin{gathered} x\times 9.11\times {10}^{-28}g=1\times 1 \\ \Rightarrow x={\displaystyle \frac{1}{9.11\times {10}^{-28}g}}=1.098\times {10}^{27} \end{gathered}$$
$1.098\times {10}^{27}$electrons weigh 1 gram.

(ii) Mass and charge of one mole of electrons.
One mole of electrons contains $6.023\times {10}^{23}$ electrons
Mass of an electron is $9.11\times {10}^{-28}g$
Mass of $6.023\times {10}^{23}$ electrons is
$$\begin{gathered} 6.023\times {10}^{23}\times 9.11\times {10}^{-28}g \\ \Rightarrow 5.486\times {10}^{-4}g \end{gathered}$$
Charge of an electron is $1.602\times {10}^{-19}C$
Charge of $6.023\times {10}^{23}$ electrons is
$$\begin{gathered} 6.023\times {10}^{23}\times 1.602\times {10}^{-19}C \\ \Rightarrow 9.648\times {10}^{4}C \end{gathered}$$

Note: Do not confuse between one mole and one molecule. One mole is used to measure the quantity of a substance like no. of atoms or no. of molecules whereas one molecule is defined as the combination of two or more atoms of the same element or different element. One mole contains avogadro's number of molecular entities (atoms, electrons, molecules etc).