Question

What is the total charge in coulombs of$\mathbf{75}\mathbf{.0}\mathbf{\text{kg}}$of electrons?

Short answer

$q=-1.32\times {10}^{13}C$

Step-by-step solution

Given

Mass of collection of electrons is,$M=75.0\text{\hspace{0.17em}kg}$

Understanding the concept

Charges are quantized. It means the charge on any object is equal to the integer multiple of an elementary charge. The charge will always be present in an integer number and never as a fraction.

Calculate the total charge in coulombs of 75.0 kg of electrons

The mass of an electron is$m=9.11\times {10}^{-31}\text{kg}$, so the number of electrons in a collection with total mass$M=75.0\text{\hspace{0.17em}kg}$.

$\begin{array}{c}n=\frac{M}{m}\\ =\frac{75.0\text{kg}}{9.11\times {10}^{-31}\text{kg}}\\ =8.23\times {10}^{+31}\text{electrons}\end{array}$

The total charge of the collection is,

$\begin{array}{c}q=-ne\\ =-(8.23\times {10}^{+31}\text{electrons})(1.60\times {10}^{-19}\text{C})\\ =-1.32\times {10}^{13}\text{C}\end{array}$

Therefore,the total charge of the collection is$1.32\times {10}^{13}\text{C}$.