Solved Problem on Electric Charge
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The atomic number of a monatomic metal is equal to z. Consider a block of mass m of this metal. If the metal is neutral, the total number of positive charges equals the total number of negative charges, that is, the total number of electrons equals the total number of protons. Obtain an expression for calculating the positive charge on this material.
Problem data:
- Metal atomic number: z;
- Mass of block: m.
The positive electric charge q of an atom of this material will be the atomic number z multiplied by the elementary charge e
\[
\begin{gather}
q=ze \tag{I}
\end{gather}
\]
The total charge Q will be the number of atoms of the material N multiplied by the charge of
each atom q
\[
\begin{gather}
Q=Nq \tag{II}
\end{gather}
\]
substituting expression (II) into expression (I)
\[
\begin{gather}
Q=Nze \tag{III}
\end{gather}
\]
The number of moles n of this metal will be the mass of material m divided by the molar mass
of material M
\[
\begin{gather}
\bbox[#99CCFF,10px]
{n=\frac{m}{M}} \tag{IV}
\end{gather}
\]
The number of atoms of the material N will be the number of moles n multiplied by
Avogadro's Number NA
\[
\begin{gather}
N=nN_{A} \tag{V}
\end{gather}
\]
substituting the expression (IV) into the expression (V)
\[
\begin{gather}
N=\frac{m}{M}N_{A} \tag{VI}
\end{gather}
\]
substituting expression (VI) into expression (III)
\[
\begin{gather}
\bbox[#FFCCCC,10px]
{Q=\frac{m}{M}N_{A}ze}
\end{gather}
\]
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