Question

A body has a charge of $-2\mu C$. If it has $2.5\times {10}^{13}$ protons, then how many electrons the body has?

Answer 1

Step 1. Given data:

Charge on a body = $-2\mu C$

Number of protons = $2.5\times {10}^{13}$

Step 2. Formula used:

Total charge on the body is equal to total charge due to protons and charge due to electrons.

$Q=p{e}_{+}+n{e}_{-}$………….$\left(1\right)$

where $p$ and $n$ are no. of protons and no. of electrons respectively, $e$ = charge, ($1.6\times {10}^{-19}C$), $Q$ = Total charge,

Step 3. Calculations:

Putting the given values in equation $\left(1\right)$, we get

$-2\times {10}^{-6}=\left(2.5\times {10}^{13}\times 1.6\times {10}^{-19}\right)+\left(n\times \left(-1.6\times {10}^{-19}\right)\right)$

Since charge on proton is positive and charge on electron is negative.

Or $$\begin{gathered} \frac{\left(-2\times {10}^{-6}\right)}{\left(1.6\times {10}^{-19}\right)}=\left(2.5\times {10}^{13}-n\right) \\ \Rightarrow -1.25\times {10}^{13}=2.5\times {10}^{13}-n \\ \Rightarrow n=3.75\times {10}^{13} \end{gathered}$$

Hence, the body has $3.75\times {10}^{13}$numbers of electrons.