91Ó°ÊÓ

A body is said to be charged when it has unequal number of electrons and protons. If the body has greater number of electrons than protons, the body is said to be negatively charged.

According to the quantization of charge,

Q = ne

Here, Q is the total charge on the body due to excess electrons (Q=-5.00 nC) , is the number of electrons responsible for the negative charge on the body, and is the charge on electron $\left(e=-1.6×{10}^{-19}C\right)$.

The number of electrons responsible for the negative charge on body is,

$n=\frac{Q}{e}$

Substituting all known values,

$$\begin{gathered} n=\frac{\left(-5.00nC\right)}{\left(1.6×{10}^{-19}C\right)} \\ =3.125×{10}^{10} \end{gathered}$$

The total number of electrons on a negatively charged body is,

n_t = n_e + n

Here, n is the total number of electrons on an negatively charged body, n_e is the number of electrons to neutralize the charge of protons $\left(n_e=1.0000×{10}^{12}\right)$ , and n is the number of electrons responsible for negative charge on the body $\left(n=3.125×{10}^{10}\right)$.

Substituting all known values,

$$\begin{gathered} n_t=\left(1.0000×{10}^{12}\right)+\left(3.1250×{10}^{10}\right) \\ =1.0312×{10}^{12} \end{gathered}$$

Hence, the number of electrons in the speck of dust is $1.0312×{10}^{12}$.