Question

A certain lightning bolt moves 40.0 C of charge. How many fundamental units of charge $\left|q_e\right|$is this?

Short answer

40.0 C of charge has $2.5\times {10}^{20}$fundamental unit of charge.

Step-by-step solution

Quantization of charge

According to the quantization of charge, all charges are made of combination of fundamental unit of charge.In other words, all charged objects in nature are integral multiple of the fundamental quantity of charge. Mathematically,

$Q=n\left|q_e\right|..........(1.1)$

Here, Q is the total charge on a charged object, n is the integer or the number of fundamental units of charge, and $\left|q_e\right|$is the fundamental unit of charge.

Number of fundamental units of charge in lightning bolt

The number of fundamental units of charge can be calculated using equation (1.1).

Rearranging equation (1.1) in order to get an expression for the number of fundamental units of charge.

$n=\frac{Q}{\left|q_e\right|}$

Here, Q is the total charge moved by lightning bolt (Q = 40.0 C) , and $\left|q_e\right|$is the fundamental unit of charge $\left(\left|q_e\right|=1.6\times {10}^{-19}C\right)$.

Substituting all known values,

$$\begin{gathered} n=\frac{40.0C}{1.6\times {10}^{-19}C} \\ =2.5\times {10}^{20}C \end{gathered}$$

Hence, 40.0 C of charge has $2.5\times {10}^{20}$fundamental unit of charge.