What net charge would you place on a 100 g piece of sulfur if you put an extra electron on 1 in 10¹² of its atoms? (Sulfur has an atomic mass of 32.1.)

• Mass of piece of sulphur is 100 g
• Fraction of extra electrons is $\frac{1}{{10}^{12}}$

• Atomic mass of sulphur is 32.1

When there is imbalance in the number of electron and proton in a body, then it is said to be charged. If a body gains extra electron, the body is said to be negatively charged.

The number of moles of sulfur is,

$N=\frac{m}{M}$

Here, Nis the number of moles of sulfur, mis the mass of the sulfur piece (m= 100 g) , and is the molar mass of the sulfur (M= 32.1 g ) .

Substituting all known values,

$$\begin{gathered} N=\frac{100g}{32.1g} \\ =3.115 \end{gathered}$$

The number of sulfur atom is,

$$\begin{gathered} N_a=\left(3.115\right)\times \left(6.022\times {10}^{23}\right) \\ =1.876\times {10}^{24} \end{gathered}$$

Since, there is 1 extra electron on every 10¹² atom. Therefore, the number of extra electrons is,

$$\begin{gathered} n=\frac{1.876\times {10}^{24}}{{10}^{12}} \\ =1.876\times {10}^{12} \end{gathered}$$

According to the quantization of charge,

Q = ne

Here, Q is the net charge, n is the number of extra electron $\left(n=1.876\times {10}^{12}\right)$ , and e is the charge on an electron $\left(e=-1.6\times {10}^{-19}\mathrm{C}\right)$.

Substituting all known values,

$$\begin{gathered} Q=\left(1.876\times {10}^{12}\right)\times \left(-1.6\times {10}^{-19}C\right) \\ =3.00\times {10}^{-7}C\times \left(\frac{1\mu C}{{10}^{-6}C}\right) \\ =-0.300\mu C \end{gathered}$$

Hence, the net charge on 100 g of piece of sulfur, if it has an extra 1 electron in 10¹² of its atoms, is $-0.300\mu C$.