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A paisa coin is made up of $\mathrm{Al - Mg}$ alloy and weighs $0.75\, g$. It has a square shape and its diagonal measures $17$ $\mathrm{mm}$. It is electrically neutral and contains equal amounts of positive and negative charges.
Solution
Mass of coin $\mathrm{W}=0.79 \mathrm{~g}$
Molar mass of $\mathrm{Al}=26.9815 \mathrm{~g}$
Avogadro number $\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}$
No. of atoms in $26.9815 \mathrm{~g}=6.023 \times 10^{23}$
No. of atoms in $0.75 \mathrm{~g}=\mathrm{N}=?$
$\mathrm{N} =\frac{6.023 \times 10^{23} \times 0.75}{26.9815}$ $=0.16742 \times 10^{23}$ $=1.6742 \times 10^{22}$
Atomic no. of $\mathrm{Al}, \mathrm{Z}=13$. Hence, there are 13 protons and 13 electrons.
$\therefore$ Amount of positive and negative charge in one coin,
$\mathrm{Q}=\mathrm{NZe}$
$=1.6742 \times 10^{23} \times 13 \times 1.6 \times 10^{-19}$
$=3.48 \times 10^{4} \mathrm{C}$
$\therefore \mathrm{Q} =\pm 3.48 \times 10^{4} \mathrm{C}$
This amount is very large hence, we can conclude that there are positive and negative charges in large amount in neutral matter.
