Question

The electrostatic force of repulsion between two equal positively charged ions is $51.84\times {10}^{-9}N$, when they are separated by a distance of $0.4nm$. How many electrons are missing from each ion?

• A. $6$
• B. $5$
• C. $7$
• D. $3$

Answer 1

The correct option is A $6$

$q_1=q_2=q\left(say\right)$

$r=0.4nm=4\times {10}^{-10}m$

$F=51.84\times {10}^{-9}N$

$F=\frac{q_1{q}_2}{4\pi {ϵ}_o{r}^2}$

$⟹9\times {10}^9\times \frac{q^2}{16\times {10}^{-20}}=51.84\times {10}^{-9}$

$⟹q^2=16\times 5.76\times {10}^{-38}$

$⟹q=4\times 2.4\times {10}^{-19}C$

N=number of electrons

$q=Ne⟹N=\frac{q}{e}$

$N=\frac{4\times 2.4\times {10}^{-19}}{1.6\times {10}^{-19}}$

$⟹N=6$