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?

• A. $1.25\times {10}^{13}$
• B. $2.5\times {10}^{13}$
• C. $3.75\times {10}^{13}$
• D. None of these

Answer 1

The correct option is C $3.75\times {10}^{13}$

$\text{Step 1: Quantization of charge}$

Charge on the body is always quantized.

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.

$\text{Step 2: Substitute the values}$

From equation $\left(1\right)$

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

$\Rightarrow \frac{-2\times {10}^{-6}}{1.6\times {10}^{-19}}=2.5\times {10}^{13}-n$

$\Rightarrow -1.25\times {10}^{13}=2.5\times {10}^{13}-n$
$\Rightarrow n=3.75\times {10}^{13}$ electrons

Hence, Option(C) is correct.