(II) What is the total charge of all the electrons in a 12-kg bar of gold? What is the net charge of the bar? (Gold has 79 electrons per atom and an atomic mass of 197 u.)

Electric charge is a basic property of matter that causes small objects to attract or repel each other. The charge is quantised in nature and the electronic charge is the basic unit of charge.

The net quantity of charge is given as:

\(Q = ne\) … (i)

Here, n is the number of electrons and e is the electronic charge.

The mass of the gold bar is, \(m = 12\;{\rm{kg}}\)

The number of electrons per atom for gold is, \(n = 79\)

The atomic mass of gold is, \({m_{\rm{A}}} = 197\,{\rm{u}}\)

The mass of the gold atom in kg is,

\(\begin{array}{c}{m_{\rm{g}}} = 197\;{\rm{u}} \times \frac{{1.66 \times {{10}^{ - 27}}\;{\rm{kg}}}}{{1\;{\rm{u}}}}\\{m_{\rm{g}}} = 327.02 \times {10^{ - 27}}\;{\rm{kg}}\end{array}\)

The total number of gold atoms in the bar is,

\(\begin{array}{c}{n_{\rm{g}}} = \frac{m}{{{m_{\rm{g}}}}}\\{n_{\rm{g}}} = \frac{{12\;{\rm{kg}}}}{{327.02 \times {{10}^{ - 27}}\;{\rm{kg}}}}\\{n_{\rm{g}}} = 3.67 \times {10^{25}}\end{array}\)

The expression for the total charge of all the electrons is,

\(Q = {n_{\rm{g}}}\left( {ne} \right)\)

Here, e is the electronic charge.

\(\begin{array}{c}Q = \left( {3.67 \times {{10}^{25}}} \right)\left( {79} \right)\left( { - 1.6 \times {{10}^{ - 19}}\;{\rm{C}}} \right)\\Q = 4.6 \times {10^8}\;{\rm{C}}\end{array}\)

Thus, the total charge of all the electrons in the bar is \( - 4.6 \times {10^8}\;{\rm{C}}\).

In a neutral atom, there is the same number of electrons and protons. The negative charge of electrons will cancel out by the positive charge of protons as they both have the same charge, but the polarity is the opposite.

Thus, the net charge of the bar is zero.