# How many electrons give a charge of -3.30 nc?

## Question:

How many electrons give a charge of -3.30 nc?

## Charge and Electrons:

The ratio of the charge Q of the given substance to the charge of one electron is known as the number of electrons of the substance. The mathematical representation by this definition for the number of electrons n is:

{eq}\displaystyle n=\frac{Q}{e} {/eq}, where,

• e is the charge of the electron and it is equal to {eq}1.6\times 10^{-19} {/eq} coulombs.

Given:

• The value of the total charge is {eq}Q= -3.30\ nc {/eq}.

The negative sign shows the polarity of the charge. The value of the given charge in coulombs is:

{eq}\begin{align*} \displaystyle Q&= 3.30\ nc\times \frac{10^{-9}\ C}{1\ nc}\\ &= 3.30\times 10^{-9}\ C\\ \end{align*} {/eq}

Plugging {eq}Q= 3.30\times 10^{-9}\ C {/eq} and {eq}e= 1.6\times 10^{-19}\ C {/eq} in the formula of the number of electrons and simplifying it, we get:

{eq}\begin{align*} \displaystyle n&=\displaystyle \frac{Q}{e}\\ &=\displaystyle \frac{3.30\times 10^{-9}\ C}{1.6\times 10^{-19}\ C}\\ &=\displaystyle \frac{3.30\times 10^{-9+19}}{1.6}\\ &=\boxed{\displaystyle 2.0625\times 10^{10}}\\ \end{align*} {/eq} 